EXHIBIT 12 B1

                  CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER

                                 CERTIFICATIONS

I, Ronald E. Robison, certify that:

1.   I have reviewed this report on Form N-CSR of Morgan Stanley New York
     Municipal Money Market Trust;

2.   Based on my knowledge, this report does not contain any untrue statement of
     a material fact or omit to state a material fact necessary to make the
     statements made, in light of the circumstances under which such statements
     were made, not misleading with respect to the period covered by this
     report;

3.   Based on my knowledge, the financial statements and other financial
     information included in this report, fairly present in all material
     respects the financial condition, results of operations, changes in net
     assets, and cash flows (if the financial statements are required to include
     a statement of cash flows) of the registrant as of, and for, the periods
     presented in this report;

4.   The registrant's other certifying officers and I are responsible for
     establishing and maintaining disclosure controls and procedures (as defined
     in Rule 30a-3(c) under the Investment Company Act of 1940) and internal
     control over financial reporting (as defined in Rule 30a-3(d) under the
     Investment Company Act of 1940) for the registrant and have:

a)   designed such disclosure controls and procedures, or caused such disclosure
     controls and procedures to be designed under our supervision, to ensure
     that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

b)   designed such internal control over financial reporting, or caused such
     internal control over financial reporting to be designed under our
     supervision, to provide reasonable assurance regarding the reliability of
     financial reporting and the preparation of financial statements for
     external purposes in accordance with generally accepted accounting
     principles;

c)   evaluated the effectiveness of the registrant's disclosure controls and
     procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of a date
     within 90 days prior to the filing date of this report based on such
     evaluation; and

d)   disclosed in this report any change in the registrant's internal control
     over financial reporting that occurred during the registrant's most recent
     fiscal half-year (the registrant's second fiscal half-year in the case of
     an annual report) that has materially affected, or is reasonably likely to
     materially affect, the registrant's internal control over financial
     reporting; and

5.   The registrant's other certifying officer(s) and I have disclosed to the
     registrant's auditors and the audit committee of the registrant's board of
     directors (or persons performing the equivalent functions):


                                        4



a)   all significant deficiencies and material weaknesses in the design or
     operation of internal control over financial reporting which are reasonably
     likely to adversely affect the registrant's ability to record, process,
     summarize, and report financial information; and

b)   any fraud, whether or not material, that involves management or other
     employees who have a significant role in the registrant's internal controls
     over financial reporting.

Date: August 10, 2006


                                        /s/ Ronald E. Robison
                                        ----------------------------------------
                                        Ronald E. Robison
                                        Principal Executive Officer


                                        5



                                                                   EXHIBIT 12 B2

                  CERTIFICATION OF PRINCIPAL FINANCIAL OFFICER

                                 CERTIFICATIONS

I, Francis Smith, certify that:

1.   I have reviewed this report on Form N-CSR of Morgan Stanley New York
     Municipal Money Market Trust;

2.   Based on my knowledge, this report does not contain any untrue statement of
     a material fact or omit to state a material fact necessary to make the
     statements made, in light of the circumstances under which such statements
     were made, not misleading with respect to the period covered by this
     report;

3.   Based on my knowledge, the financial statements and other financial
     information included in this report, fairly present in all material
     respects the financial condition, results of operations, changes in net
     assets, and cash flows (if the financial statements are required to include
     a statement of cash flows) of the registrant as of, and for, the periods
     presented in this report;

4.   The registrant's other certifying officers and I are responsible for
     establishing and maintaining disclosure controls and procedures (as defined
     in Rule 30a-3(c) under the Investment Company Act of 1940) and internal
     control over financial reporting (as defined in Rule 30a-3(d) under the
     Investment Company Act of 1940) for the registrant and have:

a)   designed such disclosure controls and procedures, or caused such disclosure
     controls and procedures to be designed under our supervision, to ensure
     that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

b)   designed such internal control over financial reporting, or caused such
     internal control over financial reporting to be designed under our
     supervision, to provide reasonable assurance regarding the reliability of
     financial reporting and the preparation of financial statements for
     external purposes in accordance with generally accepted accounting
     principles;

c)   evaluated the effectiveness of the registrant's disclosure controls and
     procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of a date
     within 90 days prior to the filing date of this report based on such
     evaluation; and

d)   disclosed in this report any change in the registrant's internal control
     over financial reporting that occurred during the registrant's most recent
     fiscal half-year (the registrant's second fiscal half-year in the case of
     an annual report) that has materially affected, or is reasonably likely to
     materially affect, the registrant's internal control over financial
     reporting; and

5.   The registrant's other certifying officer(s) and I have disclosed to the
     registrant's auditors and the audit committee of the registrant's board of
     directors (or persons performing the equivalent functions):


                                        6



a)   all significant deficiencies and material weaknesses in the design or
     operation of internal control over financial reporting which are reasonably
     likely to adversely affect the registrant's ability to record, process,
     summarize, and report financial information; and

b)   any fraud, whether or not material, that involves management or other
     employees who have a significant role in the registrant's internal controls
     over financial reporting.

Date: August 10, 2006


                                        /s/ Francis Smith
                                        ----------------------------------------
                                        Francis Smith
                                        Principal Financial Officer


                                        7