Morgan Stanley Us Government Money Market Trust N-CSRS Certified semi-annual shareholder report (management investment company)

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED
MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-03326

Morgan Stanley U.S. Government Money Market Trust

(Exact name of registrant as specified in charter)

522 Fifth Avenue, New York, New York	10036
(Address of principal executive offices)	(Zip code)

Randy Takian
522 Fifth Avenue, New York, New York 10036
(Name and address of agent for service)

Registrant’s telephone number, including area code: 212-296-6990

Date of fiscal year end: January 31, 2009

Date of reporting period: July 31, 2008

Item 1 — Report to Shareholders

INVESTMENT MANAGEMENT

Welcome, Shareholder:

In this report, you’ll learn about how your investment in Morgan Stanley U.S. Government Money Market Trust performed during the semiannual period. We will provide an overview of the market conditions, and discuss some of the factors that affected performance during the reporting period. In addition, this report includes the Fund’s financial statements and a list of Fund investments.

This material must be preceded or accompanied by a prospectus for the fund being offered.

Market forecasts provided in this report may not necessarily come to pass. There is no assurance that a mutual fund will achieve its investment objective. An investment in a money market fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Although the fund seeks to preserve the value of an investment at $1.00 per share, it is possible to lose money by investing in the fund. Please see the prospectus for more complete information on investment risks.

Fund Report

For the six months ended July 31, 2008

Market Conditions

Credit and liquidity constraints, coupled with growing concerns about an economic recession made for an extremely volatile market throughout the six-month period under review. The Federal Open Market Committee (FOMC) continued in its efforts to support both the market and the economy, including reducing the federal funds target rate an additional 100 basis points to 2.00 percent. Although the FOMC remains concerned about the weakness in the U.S. economy, they are increasingly worried about inflation. In fact, Federal Reserve Bank of Dallas, President Richard Fisher said he sees the U.S. economy slowing down in the near term, but not heading into recession, with inflation the greatest risk to the economy. As a result, despite continued economic weakness, the FOMC left interest unchanged at its last meeting of the period in June.

U.S. economic growth, as measured by gross domestic product (GDP), rose just 1.9 percent in the second quarter of 2008, up slightly from 0.9 percent in the previous quarter. Job growth, as measured by non-farm payrolls, contracted in the second quarter, and has declined each month since January. July consumer confidence data, up slightly from June, remained near historically low levels. However, the Institute for Supply Management (ISM) manufacturing index measured 50 for July, slightly above expectations, and the second consecutive month at or above 50 since January of this year. (An index reading above 50 indicates the economy is expanding.)

Performance Analysis

As of July 31, 2008, Morgan Stanley U.S. Government Money Market Trust had net assets of approximately $1.22 billion and an average portfolio maturity of 42 days. For the six-month period ended July 31, 2008, the Fund provided a total return of 1.06 percent. For the seven-day period ended July 31, 2008, the Fund provided an effective annualized yield of 1.76 percent and a current yield of 1.74 percent, while its 30-day moving average yield for July was 1.73 percent. Past performance is no guarantee of future results.

Throughout the reporting period, the Fund continued to seek high liquidity and preservation of capital while generating a yield reflecting prevailing money market conditions. To do this, the management team continued its long-standing policy of purchasing high quality, liquid, money market securities and repurchase agreements. Reflecting this conservative approach, the Fund’s portfolio did not contain any derivative securities during the reporting period.

There is no guarantee that any sectors mentioned will continue to perform as discussed herein or that securities in such sectors will be held by the Fund in the future.

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PORTFOLIO COMPOSITION as of 07/31/08
U.S. Government Agencies - Floating Rate Notes	44	.7%
U.S. Government Agencies - Discount Notes	24	.3
U.S. Government Agencies - Debenture Bonds	23	.1
Repurchase Agreements	7	.9

MATURITY SCHEDULE as of 07/31/08
	1	- 30 Days	61	.2%
	31	- 60 Days	15	.3
	61	- 90 Days	12	.0
	91	- 120 Days	2	.9
	121	+Days	8	.6

Subject to change daily. Provided for informational purposes only and should not be deemed a recommendation to buy or sell the securities mentioned above. Portfolio composition and maturity schedule are as a percentage of total investments. Morgan Stanley is a full-service securities firm engaged in securities trading and brokerage activities, investment banking, research and analysis, financing and financial advisory services.

Investment Strategy

The Fund will invest in high quality, short-term U.S. government securities. The Fund’s “Investment Adviser,” Morgan Stanley Investment Advisors Inc., seeks to maintain the Fund’s share price at $1.00. The share price remaining stable at $1.00 means that the Fund would preserve the principal value of your investment.

An investment in the Fund is not insured or guaranteed by the Federal Deposit Insurance Corporation or any other government agency. Although the Fund seeks to preserve the value of your investment at $1.00 per share, it is possible to lose money by investing in the Fund.

For More Information About Portfolio Holdings

Each Morgan Stanley fund provides a complete schedule of portfolio holdings in its semiannual and annual reports within 60 days of the end of the fund’s second and fourth fiscal quarters. The semiannual reports and the annual reports are filed electronically with the Securities and Exchange Commission (SEC) on Form N-CSRS and Form N-CSR, respectively. Morgan Stanley also delivers the semiannual and annual reports to fund shareholders and makes these reports available on its public web site, www.morganstanley.com. Each Morgan Stanley fund also files a complete schedule of portfolio holdings with the SEC for the fund’s first and third fiscal quarters on Form N-Q. Morgan Stanley does not deliver the reports for the first and third fiscal quarters to shareholders, nor are the reports posted to the Morgan Stanley public web site. You may, however,

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obtain the Form N-Q filings (as well as the Form N-CSR and N-CSRS filings) by accessing the SEC’s web site, http://www.sec.gov. You may also review and copy them at the SEC’s public reference room in Washington, DC. Information on the operation of the SEC’s public reference room may be obtained by calling the SEC at (800) SEC-0330. You can also request copies of these materials, upon payment of a duplicating fee, by electronic request at the SEC’s e-mail address (publicinfo@sec.gov) or by writing the public reference section of the SEC, Washington, DC 20549-0102.

Householding Notice

To reduce printing and mailing costs, the Fund attempts to eliminate duplicate mailings to the same address. The Fund delivers a single copy of certain shareholder documents, including shareholder reports, prospectuses and proxy materials, to investors with the same last name who reside at the same address. Your participation in this program will continue for an unlimited period of time unless you instruct us otherwise. You can request multiple copies of these documents by calling (800) 869-NEWS, 8:00 a.m. to 8:00 p.m., ET. Once our Customer Service Center has received your instructions, we will begin sending individual copies for each account within 30 days.

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Expense Example

As a shareholder of the Fund, you incur ongoing costs, including advisory fees; distribution and shareholder servicing; and other Fund expenses. This example is intended to help you understand your ongoing costs (in dollars) of investing in the Fund and to compare these costs with the ongoing costs of investing in other mutual funds.

The example is based on an investment of $1,000 invested at the beginning of the period and held for the entire period 02/01/08 – 07/31/08.

Actual Expenses

The first line of the table below provides information about actual account values and actual expenses. You may use the information in this line, together with the amount you invested, to estimate the expenses that you paid over the period. Simply divide your account value by $1,000 (for example, an $8,600 account value divided by $1,000 = 8.6), then multiply the result by the number in the first line under the heading entitled “Expenses Paid During Period” to estimate the expenses you paid on your account during this period.

Hypothetical Example for Comparison Purposes

The second line of the table below provides information about hypothetical expenses based on the Fund’s actual expense ratio and an assumed rate of return of 5% per year before expenses, which is not the Fund’s actual return. The hypothetical account values and expenses may not be used to estimate the actual ending account balance or expenses you paid for the period. You may use this information to compare the ongoing cost of investing in the Fund and other funds. To do so, compare this 5% hypothetical example with the 5% hypothetical examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your ongoing costs only. Therefore, the second line of the table is useful in comparing ongoing costs, and will not help you determine the relative total cost of owning different funds that have transactional costs, such as sales charges (loads), and redemption fees, or exchange fees.

	Beginning		Ending		Expenses Paid
	Account Value		Account Value		During Period @
					02/01/08 –
	02/01/08		07/31/08		07/31/08
Actual (1.06% return)	$	1,000.00	$	1,010.60	$	3.25
Hypothetical (5% annual return before expenses)	$	1,000.00	$	1,021.63	$	3.27

 @   Expenses are equal to the Fund’s annualized expense ratio of 0.65% multiplied by the average account value over the period, multiplied by 182/366 (to reflect the one-half year period).

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Investment Advisory Agreement Approval

Nature, Extent and Quality of Services

The Board reviewed and considered the nature and extent of the investment advisory services provided by the Investment Adviser under the Advisory Agreement, including portfolio management, investment research and fixed income securities trading. The Board also reviewed and considered the nature and extent of the non-advisory, administrative services provided by the Fund’s Administrator under the Administration Agreement, including accounting, clerical, bookkeeping, compliance, business management and planning, and the provision of supplies, office space and utilities at the Investment Adviser’s expense. (The Investment Adviser and the Administrator together are referred to as the “Adviser” and the Advisory and Administration Agreements together are referred to as the “Management Agreement.”) The Board also compared the nature of the services provided by the Adviser with similar services provided by non-affiliated advisers as reported to the Board by Lipper Inc. (“Lipper”).

The Board reviewed and considered the qualifications of the portfolio managers, the senior administrative managers and other key personnel of the Adviser who provide the advisory and administrative services to the Fund. The Board determined that the Adviser’s portfolio managers and key personnel are well qualified by education and/or training and experience to perform the services in an efficient and professional manner. The Board concluded that the nature and extent of the advisory and administrative services provided were necessary and appropriate for the conduct of the business and investment activities of the Fund. The Board also concluded that the overall quality of the advisory and administrative services was satisfactory.

Performance Relative to Comparable Funds Managed by Other Advisers

On a regular basis, the Board reviews the performance of all funds in the Morgan Stanley Fund Complex, including the Fund, compared to their peers, paying specific attention to the underperforming funds. In addition, the Board specifically reviewed the Fund’s performance for the one-, three- and five-year periods ended December 31, 2007, as shown in a report provided by Lipper (the “Lipper Report”), compared to the performance of comparable funds selected by Lipper (the “performance peer group”). The Board discussed with the Adviser the performance goals and the actual results achieved in managing the Fund. The Board concluded that the Fund’s performance was competitive with that of its performance peer group.

Fees Relative to Other Proprietary Funds Managed by the Adviser with Comparable Investment Strategies

The Board noted that the Adviser did not manage any other proprietary funds with investment strategies substantially comparable to the Fund.

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Fees and Expenses Relative to Comparable Funds Managed by Other Advisers

The Board reviewed the advisory and administrative fee (together, the “management fee”) rate and total expense ratio of the Fund as compared to the average management fee rate and average total expense ratio for funds, selected by Lipper (the “expense peer group”), managed by other advisers with investment strategies comparable to those of the Fund, as shown in the Lipper Report. The Board noted that the management fee rate and total expense ratio were higher than those of the expense peer group, and Fund’s management fee rate and total expense ratio were acceptable given the quality of services provided.

Breakpoints and Economies of Scale

The Board reviewed the structure of the Fund’s management fee schedule under the Management Agreement and noted that it includes breakpoints. The Board also reviewed the level of the Fund’s management fee and noted that the fee, as a percentage of the Fund’s net assets, would decrease as net assets increase because the management fee includes breakpoints. The Board concluded that the Fund’s management fee would reflect economies of scale as assets increase.

Profitability of the Adviser and Affiliates

The Board considered information concerning the costs incurred and profits realized by the Adviser and affiliates during the last year from their relationship with the Fund and during the last two years from their relationship with the Morgan Stanley Fund Complex and reviewed with the Adviser the cost allocation methodology used to determine the profitability of the Adviser and affiliates. Based on its review of the information it received, the Board concluded that the profits earned by the Adviser and affiliates were not excessive in light of the advisory, administrative and other services provided to the Fund.

Fall-Out Benefits

The Board considered so-called “fall-out benefits” derived by the Adviser and affiliates from their relationship with the Fund and the Morgan Stanley Fund Complex, such as “float” benefits derived from handling of checks for purchases and sales of Fund shares, through a broker-dealer affiliate of the Adviser. The Board also considered that a broker-dealer affiliate of the Adviser receives from the Fund 12b-1 fees for distribution and shareholder services. The Board concluded that the float benefits were relatively small and the 12b-1 fees were competitive with those of other broker-dealers.

Soft Dollar Benefits

The Board considered whether the Adviser realizes any benefits from commissions paid to brokers who execute securities transactions for the Fund (“soft dollars”). The Board noted that the Fund invests only in fixed income securities, which do not generate soft dollars.

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Adviser Financially Sound and Financially Capable of Meeting the Fund’s Needs

The Board considered whether the Adviser is financially sound and has the resources necessary to perform its obligations under the Management Agreement. The Board concluded that the Adviser has the financial resources necessary to fulfill its obligations under the Management Agreement.

Historical Relationship Between the Fund and the Adviser

The Board also reviewed and considered the historical relationship between the Fund and the Adviser, including the organizational structure of the Adviser, the policies and procedures formulated and adopted by the Adviser for managing the Fund’s operations and the Board’s confidence in the competence and integrity of the senior managers and key personnel of the Adviser. The Board concluded that it is beneficial for the Fund to continue its relationship with the Adviser.

Other Factors and Current Trends

The Board considered the controls and procedures adopted and implemented by the Adviser and monitored by the Fund’s Chief Compliance Officer and concluded that the conduct of business by the Adviser indicates a good faith effort on its part to adhere to high ethical standards in the conduct of the Fund’s business.

General Conclusion

After considering and weighing all of the above factors, the Board concluded that it would be in the best interest of the Fund and its shareholders to approve renewal of the Management Agreement for another year until June 30, 2009.

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Morgan Stanley U.S. Government Money Market Trust

Portfolio of Investments - July 31, 2008 (unaudited)

			ANNUALIZED
PRINCIPAL			YIELD
AMOUNT IN			ON DATE OF	MATURITY
THOUSANDS		DESCRIPTION	PURCHASE	DATE	VALUE
		U.S. Government Agencies – Floating Rate Notes (44.7%)
$	53,000	Federal Farm Credit Banks	2.06 – 2.64 (a)%	08/01/08 – 09/25/08 (b)	$	52,995,941
	354,100	Federal Home Loan Banks	1.97 – 2.79 (a)	08/01/08 – 10/24/08 (b)		354,068,507
	127,000	Federal Home Loan Mortgage Corp.	2.36 – 2.64 (a)	08/08/08 – 09/30/08 (b)		126,998,366
	10,000	Federal National Mortgage Assoc.	2.10(a)	08/01/08 (b)		10,000,000
		Total U.S. Government Agencies – Floating Rate Notes(Cost $544,062,814)				544,062,814
		U.S. Government Agencies – Discount Notes (24.4%)
	247,381	Federal Home Loan Banks	1.82 – 2.70	08/01/08 – 12/10/08		246,764,913
	37,120	Federal Home Loan Mortgage Corp.	2.15 – 2.68	08/18/08 – 12/30/08		36,934,144
	12,400	Federal National Mortgage Assoc.	2.22 – 2.36	08/20/08 -09/17/08		12,380,973
		Total U.S. Government Agencies – Discount Notes(Cost $296,080,030)				296,080,030
		U.S. Government Agencies – Debenture Bonds (23.1%)
	165,600	Federal Home Loan Banks	2.02 – 2.96	08/15/08 – 06/18/09		165,808,952
	69,422	Federal Home Loan Mortgage Corp.	2.16 – 2.56	08/14/08 – 04/07/09		69,514,278
	37,908	Federal National Mortgage Assoc.	2.00 – 2.70	08/15/08 – 01/15/09		38,039,866
	7,000	Tennessee Valley Authority	2.50	11/13/08		7,055,581
		Total U.S. Government Agencies – Debenture Bonds(Cost $280,418,677)				280,418,677
		Repurchase Agreements (7.9%)
	95,700	Barclays Capital Inc. (dated 07/31/08; proceeds $95,705,848; fully collateralized by Federal National Mortgage Assoc. 5.00% – 7.00% due 08/01/38 – 07/01/48 and Federal Home Loan Mortgage Corp. 5.50% – 7.00% due 05/01/47 – 05/01/48 valued at $98,571,000) (Cost $95,700,000)	2.20	08/01/08		95,700,000

Total Investments (Cost $1,216,261,521) (c)	100.1	%		1,216,261,521
Liabilities in Excess of Other Assets	(0.1	)		(634,725	)
Net Assets	100.0	%	$	1,215,626,796

(a)	Rates shown are rates in effect at July 31, 2008.
(b)	Date of next interest rate reset.
(c)	Cost is the same for federal income tax purposes.

See Notes to Financial Statements

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Morgan Stanley U.S. Government Money Market Trust

Financial Statements

Statement of Assets and Liabilities

July 31, 2008 (unaudited)

Assets:
Investments in securities, at value (cost $1,216,261,521)	$1,216,261,521
Cash	200,937
Receivable for:
Interest	4,721,371
Shares of beneficial interest sold	55,187
Prepaid expenses and other assets	112,628
Total Assets	1,221,351,644
Liabilities:
Payable for:
Shares of beneficial interest redeemed	4,985,081
Investment advisory fee	378,917
Distribution fee	98,072
Administration fee	49,036
Transfer agent fee	33,864
Accrued expenses and other payables	179,878
Total Liabilities	5,724,848
Net Assets	$1,215,626,796
Composition of Net Assets:
Paid-in-capital	$1,215,530,375
Accumulated undistributed net investment income	64,835
Accumulated undistributed net realized gain	31,586
Net Assets	$1,215,626,796
Net Asset Value Per Share
1,215,595,277 shares outstanding (unlimited shares authorized of $.01 par value)	$1.00

Statement of Operations

For the six months ended July 31, 2008 (unaudited)

Net Investment Income:
Interest Income	$	15,714,344
Expenses
Investment advisory fee		2,211,938
Distribution fee		571,716
Transfer agent fees and expenses		416,810
Administration fee		285,858
Shareholder reports and notices		80,034
Registration fees		44,263
Custodian fees		33,598
Professional fees		25,834
Trustees’ fees and expenses		10,837
Other		27,209
Total Expenses		3,708,097
Less: expense offset		(1,465	)
Net Expenses		3,706,632
Net Investment Income		12,007,712
Net Realized Gain		31,586
Net Increase	$	12,039,298

See Notes to Financial Statements

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Morgan Stanley U.S. Government Money Market Trust

Financial Statements

Statements of Changes in Net Assets

	FOR THE SIX			FOR THE YEAR
	MONTHS ENDED			ENDED
	JULY 31, 2008			JANUARY 31, 2008
	(unaudited)
Increase (Decrease) in Net Assets:
Operations:
Net investment income	$	12,007,712		$	33,862,226
Net realized gain		31,586			11,894
Net Increase		12,039,298			33,874,120
Dividends and Distributions to Shareholders from:
Net investment income		(12,007,789	)		(33,880,542	)
Net realized gain		—			(11,894	)
Total Dividends and Distributions		(12,007,789	)		(33,892,436	)
Net increase from transactions in shares of beneficial interest		295,758,388			140,567,525
Net Increase		295,789,897			140,549,209
Net Assets:
Beginning of period		919,836,899			779,287,690
End of Period (Including accumulated undistributed net investment income of $64,835 and $64,912, respectively)	$	1,215,626,796		$	919,836,899

See Notes to Financial Statements

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements - July 31, 2008 (unaudited)

1. Organization and Accounting Policies

Morgan Stanley U.S. Government Money Market Trust (the “Fund”) is registered under the Investment Company Act of 1940, as amended (the “Act”), as a diversified, open-end management investment company. The Fund’s investment objectives are security of principal, high current income and liquidity. The Fund was organized as a Massachusetts business trust on November 18, 1981 and commenced operations on February 17, 1982.

The following is a summary of significant accounting policies:

A. Valuation of Investments — Portfolio securities are valued at amortized cost, which approximates market value, in accordance with Rule 2a-7 under the Act.

B. Accounting for Investments — Security transactions are accounted for on the trade date (date the order to buy or sell is executed). Realized gains and losses on security transactions are determined by the identified cost method. Discounts are accreted and premiums are amortized over the life of the respective securities and are included in interest income. Interest income is accrued daily.

C. Repurchase Agreements — The Fund may invest directly with institutions in repurchase agreements. The Fund’s custodian receives the collateral, which is marked-to-market daily to determine that the value of the collateral does not decrease below the repurchase price plus accrued interest.

D. Federal Income Tax Policy — It is the Fund’s policy to comply with the requirements of Subchapter M of the Internal Revenue Code applicable to regulated investment companies and to distribute substantially all of its taxable income to its shareholders. Therefore, no provision for federal income taxes is required. The Fund files tax returns with the U.S. Internal Revenue Service, New York State and New York City. The Fund adopted the provisions of the Financial Accounting Standards Board (“FASB”) Interpretation No. 48 (“FIN 48”) Accounting for Uncertainty in Income Taxes on July 30, 2008. FIN 48 sets forth a minimum threshold for financial statement recognition of the benefit of a tax position taken or expected to be taken in a tax return. The implementation of FIN 48 did not result in any unrecognized tax benefits in the accompanying financial statements. If applicable, the Fund recognizes interest accrued related to unrecognized tax benefits in interest expense and penalties in other expenses in the Statement of Operations. Each of the tax years in the four year period ended July 31, 2008, remains subject to examination by taxing authorities.

E. Dividends and Distributions to Shareholders — The Fund records dividends and distributions to shareholders as of the close of each business day.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements - July 31, 2008 (unaudited) continued

F. Use of Estimates — The preparation of financial statements in accordance with generally accepted accounting principles requires management to make estimates and assumptions that affect the reported amounts and disclosures. Actual results could differ from those estimates.

2. Investment Advisory/Administration Agreements

Pursuant to an Investment Advisory Agreement with Morgan Stanley Investment Advisors Inc. (the “Investment Adviser”), the Fund pays the Investment Adviser an advisory fee, accrued daily and payable monthly, by applying the following annual rates to the net assets of the Fund determined as of the close of each business day: 0.45% to the portion of the daily net assets not exceeding $500 million; 0.375% to the portion of the daily net assets exceeding $500 million but not exceeding $750 million; 0.325% to the portion of the daily net assets exceeding $750 million but not exceeding $1 billion; 0.30% to the portion of the daily net assets exceeding $1 billion but not exceeding $1.5 billion; 0.275% to the portion of the daily net assets exceeding $1.5 billion but not exceeding $2 billion; 0.25% to the portion of the daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.225% to the portion of the daily net assets exceeding $2.5 billion but not exceeding $3 billion; and 0.20% to the portion of the daily net assets exceeding $3 billion.

Pursuant to an Administration Agreement with Morgan Stanley Services Company Inc. (the “Administrator”), an affiliate of the Investment Adviser, the Fund pays an administration fee, accrued daily and payable monthly, by applying the annual rate of 0.05% to the Fund’s daily net assets.

Under an agreement between the Administrator and State Street Bank and Trust Company (“State Street”), State Street provides certain administrative services to the Fund. For such services, the Administrator pays State Street a portion of the fee the Administrator receives from the Fund.

The Investment Adviser has voluntarily agreed to cap the Fund’s operating expenses through June 30, 2009, by assuming the Fund’s “other expenses” and/or waiving the Fund’s investment advisory fees, and the Fund’s Administrator has agreed to waive the administrative fees, to the extent such operating expenses exceed 0.75% of the average net assets of the Fund on an annualized basis.

3. Shareholder Service Plan

Pursuant to a Shareholder Service Plan (the “Plan”), the Fund may pay the Distributor as compensation for the provision of services to shareholders a service fee up to the rate of 0.15% on an annualized basis of the average daily net assets of the Fund.

Reimbursements for these expenses are made in monthly payments by the Fund to the Distributor, which will in no event exceed an amount equal to a payment at the annual rate of 0.15% of the Fund’s

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements - July 31, 2008 (unaudited) continued

average daily net assets during the month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal year will not be reimbursed by the Fund through payments accrued in any subsequent fiscal year. For the six months ended July 31, 2008, the distribution fee was accrued at the annual rate of 0.10%.

4. Security Transactions and Transactions with Affiliates

The cost of purchases and proceeds from sales/maturities of portfolio securities for the six months ended July 31, 2008 aggregated $43,176,906,598 and $42,903,054,757, respectively.

Morgan Stanley Trust, an affiliate of the Investment Adviser, Administrator and Distributor, is the Fund’s transfer agent.

The Fund has an unfunded noncontributory defined benefit pension plan covering certain independent Trustees of the Fund who will have served as independent Trustees for at least five years at the time of retirement. Benefits under this plan are based on factors which include years of service and compensation. The Trustees voted to close the plan to new participants and eliminate the future benefits growth due to increases to compensation after July 31, 2003. Aggregate pension costs for the six months ended July 31, 2008 included in Trustees’ fees and expenses in the Statement of Operations amounted to $2,950. At July 31, 2008, the Fund had an accrued pension liability of $59,618 which is included in accrued expenses in the Statement of Assets and Liabilities.

The Fund has an unfunded Deferred Compensation Plan (the “Compensation Plan”) which allows each independent Trustee to defer payment of all, or a portion, of the fees he or she receives for serving on the Board of Trustees. Each eligible Trustee generally may elect to have the deferred amounts credited with a return equal to the total return on one or more of the Morgan Stanley funds that are offered as investment options under the Compensation Plan. Appreciation/depreciation and distributions received from these investments are recorded with an offsetting increase/decrease in the deferred compensation obligation and do not affect the net asset value of the Fund.

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements - July 31, 2008 (unaudited) continued

5. Shares of Beneficial Interest

Transactions in shares of beneficial interest, at $1.00 per share, were as follows:

	FOR THE SIX			FOR THE
	MONTHS ENDED			YEAR ENDED
	JULY 31, 2008			JANUARY 31, 2008
	(unaudited)
Shares sold		1,424,732,668			1,602,357,214
Shares issued in reinvestment of dividends and distributions		11,895,305			33,757,219
		1,436,627,973			1,636,114,433
Shares redeemed		(1,140,869,585	)		(1,495,546,908	)
Net increase		295,758,388			140,567,525

6. Expense Offset

The expense offset represents a reduction of the fees and expenses for interest earned on cash balances maintained by the Fund with the transfer agent and custodian.

7. Risks Relating to Certain Financial Instruments

The Fund may invest in securities issued by Federal National Mortgage Association (“FNMA”) and Federal Home Loan Mortgage Corporation (“FHLMC”). Securities issued by FNMA and FHLMC are not backed by or entitled to the full faith and credit of the United States and are supported by the right of the issuer to borrow from the Treasury.

8. Fair Valuation Measurements

The Fund adopted Financial Accounting Standards Board Statement of Financial Accounting Standards No. 157, “Fair Value Measurements” (“FAS 157”), effective December 1, 2007. In accordance with FAS 157, fair value is defined as the price that the Fund would receive to sell an investment or pay to transfer a liability in a timely transaction with an independent buyer in the principal market, or in the absence of a principal market the most between (1) inputs that reflect the assumptions market participants would use in pricing an asset or liability developed based on market data obtained from sources independent of the reporting entity (observable inputs) and (2) inputs that reflect the reporting entity’s own assumptions about the assumptions market participants would use in pricing an asset or liability developed based on the best information available in the circumstances(unobservable inputs) and to establish classification of fair value measurements for disclosure purposes. Various inputs are

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Morgan Stanley U.S. Government Money Market Trust

Notes to Financial Statements - July 31, 2008 (unaudited) continued

used in determining the value of the Fund’s investments. The inputs are summarized in the three broad levels listed below.

•  Level 1 — quoted prices in active markets for identical investments

•  Level 2 — other significant observable inputs (including quoted prices for similar investments, interest rates, prepayment speeds, credit risk, etc.)

•  Level 3 — significant unobservable inputs (including the Fund’s own assumptions in determining the fair value of investments)

The inputs or methodology used for valuing securities are not necessarily an indication of the risk associated with investing in those securities. The following is a summary of the inputs used as of July 31, 2008 in valuing the Fund’s investments carried at value:

			FAIR VALUE MEASUREMENTS AT JULY 31, 2008 USING
			QUOTED PRICES IN		SIGNIFICANT		SIGNIFICANT
			ACTIVE MARKET FOR		OTHER OBSERVABLE		UNOBSERVABLE
			IDENTICAL ASSETS		INPUTS		INPUTS
	TOTAL		(LEVEL 1)		(LEVEL 2)		(LEVEL 3)
Investments in Securities	$	1,216,261,521		—	$	1,216,261,521		—

9. Accounting Pronouncement

On March 19, 2008, FASB released Statement of Financial Accounting Standards No. 161, Disclosures about Derivative Instruments and Hedging Activities, an amendment of FASB statement No. 133 (“SFAS 161”). SFAS 161 requires qualitative disclosures about objectives and strategies for using derivatives, quantitative disclosures about fair value amounts of gains and losses on derivative instruments, and disclosures about credit-risk related contingent features in derivative agreements. The application of SFAS 161 is required for fiscal years beginning after November 15, 2008 and interim periods within those fiscal years. At this time, management is evaluating the implications of SFAS 161 and its impact on the financial statements has not yet been determined.

16

Morgan Stanley U.S. Government Money Market Trust

Financial Highlights

Selected ratios and per share data for a share of beneficial interest outstanding throughout each period:

	FOR THE SIX
	MONTHS ENDED			FOR THE YEAR ENDED JANUARY 31,
	JULY 31, 2008			2008			2007			2006			2005			2004
	(unaudited)
Selected Per Share Data:
Net asset value, beginning of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Net investment income from investment operations		0.011			0.044			0.044			0.027			0.008			0.004
Less dividends from net investment income	(	0.011	)	(	0.044	)(1)	(	0.044	)(1)	(	0.027	)	(	0.008	)	(	0.004	)
Net asset value, end of period	$	1.00		$	1.00		$	1.00		$	1.00		$	1.00		$	1.00
Total Return		1.06	%(2)		4.50	%		4.49	%		2.71	%		0.78	%		0.45	%
Ratios to Average Net Assets:
Total expenses (before expense offset)		0.65	%(3)		0.75	%		0.74	%(4)		0.75	%(4)		0.73	%		0.71	%(4)
Net investment income		2.09	%(3)		4.36	%		4.36	%(4)		2.62	%(4)		0.74	%		0.43	%(4)
Supplemental Data:
Net assets, end of period, in millions		$1,216			$920			$779			$938			$1,123			$1,269

(1)	Includes capital gain distributions of less than $0.001.
(2)	Not annualized
(3)	Annualized.
(4)	If the Fund had borne all its expenses that were reimbursed or waived by the Investment Adviser and Administrator, the annualized expense and net investment income ratios, before expense offset, would have been as follows:

	EXPENSE			NET INVESTMENT
PERIOD ENDED	RATIO			INCOME RATIO
January 31, 2007		0.80	%		4.30	%
January 31, 2006		0.76			2.60
January 31, 2004		0.71			0.43

See Notes to Financial Statements

17

Morgan Stanley U.S. Government Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited)

We are required by federal law to provide you with a copy of our Privacy Policy annually.

The following Policy applies to current and former individual investors in Morgan Stanley Advisor funds. This Policy is not applicable to partnerships, corporations, trusts or other non-individual clients or account holders. Please note that we may amend this Policy at any time, and will inform you of any changes to this Policy as required by law.

We Respect Your Privacy

We appreciate that you have provided us with your personal financial information. We strive to maintain the privacy of such information while we help you achieve your financial objectives. This Policy describes what non-public personal information we collect about you, why we collect it, and when we may share it with others. We hope this Policy will help you understand how we collect and share non-public personal information that we gather about you. Throughout this Policy, we refer to the non-public information that personally identifies you or your accounts as “personal information.”

1.  What Personal Information Do We Collect About You?

To serve you better and manage our business, it is important that we collect and maintain accurate information about you. We may obtain this information from applications and other forms you submit to us, from your dealings with us, from consumer reporting agencies, from our Web sites and from third parties and other sources.

For example:

•  We may collect information such as your name, address, e-mail address, telephone/fax numbers, assets, income and investment objectives through applications and other forms you submit to us.

•  We may obtain information about account balances, your use of account(s) and the types of products and services you prefer to receive from us through your dealings and transactions with us and other sources.

•  We may obtain information about your creditworthiness and credit history from consumer reporting agencies.

•  We may collect background information from and through third-party vendors to verify representations you have made and to comply with various regulatory requirements.

•  If you interact with us through our public and private Web sites, we may collect information that you provide directly through online communications (such as an e-mail address). We may also collect information about your Internet service provider, your domain name, your computer’s operating system and Web browser, your use of our Web sites and your product and service preferences, through the use of “cookies.” “Cookies” recognize your computer each time you return to one of

18

Morgan Stanley U.S. Government Money Market Trust

An Important Notice Concerning Our U.S. Privacy Policy (unaudited) continued

our sites, and help to improve our sites’ content and personalize your experience on our sites by, for example, suggesting offerings that may interest you. Please consult the Terms of Use of these sites for more details on our use of cookies.

2.  When Do We Disclose Personal Information We Collect About You?

To provide you with the products and services you request, to serve you better and to manage our business, we may disclose personal information we collect about you to our affiliated companies and to non-affiliated third parties as required or permitted by law.

A. Information We Disclose to Our Affiliated Companies.  We do not disclose personal information that we collect about you to our affiliated companies except to enable them to provide services on our behalf or as otherwise required or permitted by law.

B. Information We Disclose to Third Parties.  We do not disclose personal information that we collect about you to non-affiliated third parties except to enable them to provide services on our behalf, to perform joint marketing agreements with other financial institutions, or as otherwise required or permitted by law. For example, some instances where we may disclose information about you to nonaffiliated third parties include: for servicing and processing transactions, to offer our own products and services, to protect against fraud, for institutional risk control, to respond to judicial process or to perform services on our behalf. When we share personal information with these companies, they are required to limit their use of personal information to the particular purpose for which it was shared and they are not allowed to share personal information with others except to fulfill that limited purpose.

3.  How Do We Protect the Security and Confidentiality of Personal Information We Collect About You?

We maintain physical, electronic and procedural security measures to help safeguard the personal information we collect about you. We have internal policies governing the proper handling of client information. Third parties that provide support or marketing services on our behalf may also receive personal information, and we require them to adhere to confidentiality standards with respect to such information.

19

  Trustees   Frank L. Bowman Michael Bozic Kathleen A. Dennis James F. Higgins Dr. Manuel H. Johnson Joseph J. Kearns Michael F. Klein Michael E. Nugent W. Allen Reed Fergus Reid   Officers   Michael E. Nugent Chairperson of the Board   Randy Takian President and Principal Executive Officer   Kevin Klingert Vice President   Dennis F. Shea Vice President   Amy R. Doberman Vice President   Carsten Otto Chief Compliance Officer   Stefanie V. Chang Yu Vice President   Francis J. Smith Treasurer and Chief Financial Officer   Mary E. Mullin Secretary   Transfer Agent   Morgan Stanley Trust Harborside Financial Center, Plaza Two Jersey City, New Jersey 07311   Independent Registered Public Accounting Firm   Deloitte & Touche LLP Two World Financial Center New York, New York 10281   Legal Counsel   Clifford Chance US LLP 31 West 52nd Street New York, NY 10019   Counsel to the Independent Trustees   Kramer Levin Naftalis & Frankel LLP 1177 Avenue of the Americas New York, NY 10036   Investment Adviser   Morgan Stanley Investment Advisors Inc. 522 Fifth Avenue New York, New York 10036     The financial statements included herein have been taken from the records of the Fund without examination by the independent auditors and accordingly they do not express an opinion thereon.   This report is submitted for the general information of the shareholders of the Fund. For more detailed information about the Fund, its fees and expenses and other pertinent information, please read its Prospectus. The Fund’s Statement of Additional Information contains additional information about the Fund, including its trustees. It is available, without charge, by calling (800) 869-NEWS.   This report is not authorized for distribution to prospective investors in the Fund unless preceded or accompanied by an effective Prospectus. Read the Prospectus carefully before investing.   Morgan Stanley Distributors Inc., member FINRA.     (c) 2008 Morgan Stanley  

INVESTMENT MANAGEMENT

Morgan Stanley

U.S. Government

Money Market Trust

DWGSAN

IU08-04806P-Y07/08

Item 2. Code of Ethics.

Not applicable for semiannual reports.

Item 3. Audit Committee Financial Expert.

Not applicable for semiannual reports.

Item 4. Principal Accountant Fees and Services

Not applicable for semiannual reports.

Item 5. Audit Committee of Listed Registrants.

Not applicable for semiannual reports.

Item 6.

(a) Refer to Item 1.

(b) Not applicable.

Item 7. Disclosure of Proxy Voting Policies and Procedures for Closed-End Management Investment Companies.

Not applicable for semiannual reports.

Item 8. Portfolio Managers of Closed-End Management Investment Companies

Applicable only to reports filed by closed-end funds.

Item 9. Closed-End Fund Repurchases

Applicable to reports filed by closed-end funds.

Item 10. Submission of Matters to a Vote of Security Holders

Not applicable.

Item 11. Controls and Procedures

(a) The Fund’s principal executive officer and principal financial officer have concluded that the Fund’s disclosure controls and procedures are sufficient to ensure that information required to be disclosed by the Fund in this Form N-CSR was recorded, processed, summarized and reported within the time periods specified in the Securities and Exchange Commission’s rules and forms, based upon such officers’ evaluation of these controls and procedures as of a date within 90 days of the filing date of the report.

(b) There were no changes in the registrant’s internal control over financial reporting that
occurred during the second fiscal quarter of the period covered by this report that has materially affected, or is reasonably likely to materially affect, the registrant’s internal control over financial reporting.

Item 12. Exhibits

(a) Code of Ethics – Not applicable for semiannual reports.

(b) A separate certification for each principal executive officer and principal financial officer of the registrant are attached hereto as part of
EX-99.CERT.

2

SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Morgan Stanley U.S. Government Money Market Trust

/s/ Randy Takian
Randy Takian
Principal Executive Officer
September 18, 2008

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

/s/ Randy Takian
Randy Takian
Principal Executive Officer
September 18, 2008

/s/ Francis Smith
Francis Smith
Principal Financial Officer
September 18, 2008

3