SCHEDULE 14A INFORMATION

          Proxy Statement Pursuant to Section 14(a) of the Securities
                    Exchange Act of 1934 (Amendment No.  )
        
Filed by the Registrant [X]

Filed by a Party other than the Registrant [_] 

Check the appropriate box:

[_]  Preliminary Proxy Statement         [_]  CONFIDENTIAL, FOR USE OF THE
                                              COMMISSION ONLY (AS PERMITTED BY
                                              RULE 14A-6(E)(2))

[X]  Definitive Proxy Statement 

[_]  Definitive Additional Materials 

[_]  Soliciting Material Pursuant to Section 240.14a-11(c) or Section 240.14a-12

               Nuveen Connecticut Premium Income Municipal Fund
- --------------------------------------------------------------------------------
               (Name of Registrant as Specified In Its Charter)


- --------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

   
Payment of Filing Fee (Check the appropriate box):

[X]  $125 per Exchange Act Rules 0-11(c)(1)(ii), 14a-6(i)(1), 14a-6(i)(2)
     or Item 22(a)(2) of Schedule 14A.

[_]  $500 per each party to the controversy pursuant to Exchange Act Rule
     14a-6(i)(3).

[_]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

   
     (1) Title of each class of securities to which transaction applies:

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     (2) Aggregate number of securities to which transaction applies:

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     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (Set forth the amount on which
         the filing fee is calculated and state how it was determined):

     -------------------------------------------------------------------------
      

     (4) Proposed maximum aggregate value of transaction:

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     (5) Total fee paid:

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[_]  Fee paid previously with preliminary materials.
     
[_]  Check box if any part of the fee is offset as provided by Exchange
     Act Rule 0-11(a)(2) and identify the filing for which the offsetting fee
     was paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.
     
     (1) Amount Previously Paid:
 
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     (2) Form, Schedule or Registration Statement No.:

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     (3) Filing Party:
      
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     (4) Date Filed:

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Notes:

 
                NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND
                  NUVEEN GEORGIA PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN MARYLAND PREMIUM INCOME MUNICIPAL FUND
               NUVEEN MASSACHUSETTS PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN MISSOURI PREMIUM INCOME MUNICIPAL FUND
              NUVEEN NORTH CAROLINA PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN VIRGINIA PREMIUM INCOME MUNICIPAL FUND
                NUVEEN WASHINGTON PREMIUM INCOME MUNICIPAL FUND
 
                 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606
                            TELEPHONE (312) 917-7700
 
                   NOTICE OF ANNUAL MEETINGS OF SHAREHOLDERS
                               NOVEMBER 16, 1995
 
                                                              September 29, 1995
 
TO THE SHAREHOLDERS OF THE ABOVE FUNDS:
 
  Notice is hereby given that the Annual Meeting of Shareholders of each of
Nuveen Connecticut Premium Income Municipal Fund, Nuveen Georgia Premium Income
Municipal Fund, Nuveen Maryland Premium Income Municipal Fund, Nuveen
Massachusetts Premium Income Municipal Fund, Nuveen Missouri Premium Income
Municipal Fund, Nuveen North Carolina Premium Income Municipal Fund, Nuveen
Virginia Premium Income Municipal Fund and Nuveen Washington Premium Income
Municipal Fund, each a Massachusetts business trust (individually, a "Fund"
and, collectively, the "Funds"), will be held in the 31st floor conference room
of John Nuveen & Co. Incorporated, 333 West Wacker Drive, Chicago, Illinois, on
Thursday November 16, 1995, at 10:00 a.m., Chicago time, for the following
purposes:
 
MATTERS TO BE VOTED ON BY ALL SHAREHOLDERS OF EACH FUND:
 
    1. To elect four (4) trustees to serve until the next Annual Meeting and
  until their successors shall have been duly elected and qualified.
 
    2. To ratify or reject the selection of Ernst & Young LLP as independent
  auditors for the fiscal year ending May 31, 1996.
 
    3. To transact such other business as may properly come before the
  Annual Meeting.
 
MATTER TO BE VOTED ON BY EACH FUND'S HOLDERS OF MUNICIPAL AUCTION RATE
CUMULATIVE PREFERRED SHARES ONLY:
 
    To elect two (2) trustees to serve until the next Annual Meeting and
  until their successors shall have been duly elected and qualified.
 
  Shareholders of record of each Fund at the close of business on September 18,
1995 are entitled to notice of and to vote at that Fund's Annual Meeting.
 
  IN ORDER TO AVOID DELAY AND ADDITIONAL EXPENSE FOR YOUR FUND, AND TO ASSURE
THAT YOUR SHARES ARE REPRESENTED, IF YOU DO NOT EXPECT TO BE PRESENT IN PERSON
AT YOUR ANNUAL MEETING, YOU ARE REQUESTED TO FILL IN, SIGN AND MAIL THE
ENCLOSED PROXY AS PROMPTLY AS POSSIBLE. NO POSTAGE IS REQUIRED IF MAILED IN THE
UNITED STATES.
 
                                       James J. Wesolowski
                                            Secretary

 
                NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND
                  NUVEEN GEORGIA PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN MARYLAND PREMIUM INCOME MUNICIPAL FUND
               NUVEEN MASSACHUSETTS PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN MISSOURI PREMIUM INCOME MUNICIPAL FUND
              NUVEEN NORTH CAROLINA PREMIUM INCOME MUNICIPAL FUND
                 NUVEEN VIRGINIA PREMIUM INCOME MUNICIPAL FUND
                NUVEEN WASHINGTON PREMIUM INCOME MUNICIPAL FUND
 
                 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606
                            TELEPHONE (312) 917-7700
 
                             JOINT PROXY STATEMENT
 
                                                              September 29, 1995
 
                              GENERAL INFORMATION
 
  This Joint Proxy Statement is furnished in connection with the solicitation
by the Board of Trustees of each of Nuveen Connecticut Premium Income Municipal
Fund ("Connecticut Premium"), Nuveen Georgia Premium Income Municipal Fund
("Georgia Premium"), Nuveen Maryland Premium Income Municipal Fund ("Maryland
Premium"), Nuveen Massachusetts Premium Income Municipal Fund ("Massachusetts
Premium"), Nuveen Missouri Premium Income Municipal Fund ("Missouri Premium"),
Nuveen North Carolina Premium Income Municipal Fund ("North Carolina Premium"),
Nuveen Virginia Premium Income Municipal Fund ("Virginia Premium") and Nuveen
Washington Premium Income Municipal Fund ("Washington Premium") (individually,
a "Fund" and, collectively, the "Funds"), of proxies to be voted at the Annual
Meeting of Shareholders of each Fund to be held on November 16, 1995 (for each
Fund, an "Annual Meeting" and, collectively, the "Annual Meetings"), and at any
and all adjournments thereof. The cost of preparing, printing and mailing the
enclosed proxy, accompanying notice and proxy statement, and all other costs in
connection with the solicitation of proxies, will be paid by the Funds pro rata
based on the number of shareholder accounts. Additional solicitation may be
made by letter, telephone or telegraph by officers of each Fund, by officers or
employees of John Nuveen & Co. Incorporated or Nuveen Advisory Corp., or by
dealers and their representatives. The Funds have engaged Tritech Services to
assist in the solicitation of proxies at a total estimated cost of $20,000.
EACH FUND WILL FURNISH, WITHOUT CHARGE, A COPY OF ITS MAY 31, 1995 ANNUAL
REPORT UPON REQUEST. SUCH WRITTEN OR ORAL REQUEST SHOULD BE DIRECTED TO SUCH
FUND AT 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606 OR BY CALLING
1-800-257-8787.
 
  On the matters coming before each Fund's Annual Meeting as to which a choice
has been specified by the shareholders of that Fund on the proxy, the shares of
that Fund will be voted accordingly. If no choice is so specified, the shares
of each Fund will be voted FOR the election of the four nominees for trustee to
be
 
                                       1

 
elected by all shareholders and the two nominees for trustee to be elected by
holders of Municipal Auction Rate Cumulative Preferred Shares
("MuniPreferred(R)"), as listed in this Joint Proxy Statement, and FOR
ratification of the selection of Ernst & Young LLP as each Fund's independent
auditors. Shareholders of any Fund who execute proxies may revoke them at any
time before they are voted by filing with that Fund a written notice of
revocation, by delivering a duly executed proxy bearing a later date, or by
attending that Annual Meeting and voting in person.
 
  The Board of Trustees of each Fund has determined that the use of this Joint
Proxy Statement for each Fund's Annual Meeting is in the best interest of each
Fund and its shareholders in light of the similar matters being considered and
voted on by the shareholders. Shareholders of each Fund will vote separately on
each proposal relating to their Fund, and a vote on a proposal by the
shareholders of one Fund will not affect the vote on the proposal by the
shareholders of another Fund.
 
  The following table indicates which shareholders are solicited with respect
to each matter:
 


                                                    COMMON
                    MATTER                          SHARES             MUNIPREFERRED
- ------------------------------------------------------------------------------------
                                                                 
  Election of Trustees by all Shareholders
  (Ms. Impellizzeri and Messrs. Franke,
    Brown and Sawers nominated)                      X                       X
- ------------------------------------------------------------------------------------
  Election of Trustees by MuniPreferred only
  (Mrs. Rosenheim and Mr. Schwertfeger
    nominated)                                                               X
- ------------------------------------------------------------------------------------
  Ratify Selection of Auditors                       X                       X

 
 
  A quorum of shareholders is required to take action at each Fund's Annual
Meeting. A majority of the shares entitled to vote at each Annual Meeting,
represented in person or by proxy, will constitute a quorum of shareholders at
that Annual Meeting, except that for the election of the two nominees for
trustee to be elected by holders of MuniPreferred, 33 1/3% of the MuniPreferred
shares entitled to vote and represented in person or by proxy will constitute a
quorum. Votes cast by proxy or in person at each Annual Meeting will be
tabulated by the inspectors of election appointed for that Annual Meeting. The
inspectors of election will determine whether or not a quorum is present at the
Annual Meeting. The inspectors of election will treat abstentions and "broker
non-votes" (i.e., shares held by brokers or nominees, typically in "street
name," as to which (i) instructions have not been received from the beneficial
owners or persons entitled to vote and (ii) the broker or nominee does not have
discretionary voting power on a particular matter) as present for purposes of
determining a quorum.
 
  For purposes of determining the approval of the matters submitted for a vote
of the shareholders of each Fund, abstentions and broker non-votes will have no
 
                                       2

 
effect on the election of trustees (the six nominees receiving the largest
number of votes will be elected) and will be treated as shares voted against
ratification of the selection of independent auditors. The details of each
proposal to be voted on by the shareholders of each Fund and the vote required
for approval of each proposal are set forth under the description of each
proposal below.
 
  As of September 18, 1995, there were issued and outstanding: 5,119,761 Common
Shares and 1,532 shares of MuniPreferred, Series TH of Connecticut Premium;
3,709,530 Common Shares and 1,112 shares of MuniPreferred, Series TH of Georgia
Premium; 10,335,353 Common Shares and 1,404 shares of MuniPreferred, Series W
and 1,760 shares of MuniPreferred, Series TH of Maryland Premium; 4,586,928
Common Shares and 1,360 shares of MuniPreferred, Series TH of Massachusetts
Premium; 2,136,537 Common Shares and 640 shares of MuniPreferred, Series TH of
Missouri Premium; 6,219,344 Common Shares and 1,872 shares of MuniPreferred,
Series TH of North Carolina Premium; 8,435,353 Common Shares and 832 shares of
MuniPreferred, Series T and 1,720 shares of MuniPreferred, Series TH of
Virginia Premium; and 2,320,051 Common Shares and 680 shares of MuniPreferred,
Series TH of Washington Premium. Those persons who were shareholders of record
at the close of business on September 18, 1995 will be entitled to one vote for
each share held.
 
  This Joint Proxy Statement is first being mailed to shareholders of the Funds
on or about September 29, 1995.
 
                      1. ELECTION OF TRUSTEES OF EACH FUND
 
  At each Fund's Annual Meeting, six (6) Trustees are to be elected to serve
until the next Annual Meeting and until their successors shall have been duly
elected and qualified. Under the terms of each Fund's organizational documents,
under normal circumstances holders of MuniPreferred are entitled to elect two
(2) trustees, and the remaining trustees are to be elected by holders of Common
Shares and MuniPreferred, voting together as a single class. The nominees for
election to the Board, all of whom currently serve as trustees, are the same
for each Fund. Table I below shows the nominees for trustee of each Fund to be
elected by holders of Common Shares and MuniPreferred, voting together as a
single class. Table II below shows the nominees for trustee of each Fund to be
elected by holders of MuniPreferred only. The affirmative vote of a plurality
of the shares present and entitled to vote at the Annual Meeting of each Fund
will be required to elect the trustees of that Fund.
 
  It is the intention of the persons named in the enclosed proxy to vote the
shares represented thereby for the election of the nominees listed below unless
the proxy is marked otherwise. Each of the nominees has agreed to serve as a
trustee of each Fund if elected; however, should any nominee become unable or
unwilling
 
                                       3

 
to accept nomination or election, the proxies for each Fund will be voted for
one or more substitute nominees designated by that Fund's present Board of
Trustees.
 
  Tables I and II below show each nominee's age, principal occupations and
other business affiliations, the year in which each nominee was first elected
or appointed a trustee of each Fund and the number of Common Shares of the
Funds and of all Nuveen funds (excluding money market funds) that each nominee
beneficially owned as of September 1, 1995. All of the nominees were last
elected to each Board of Trustees at the 1994 annual meeting of shareholders.
 
  The trustees mourn the recent passing of John E. O'Toole, a trustee since
each Fund's organization. There is currently a vacancy on the Board of Trustees
of each Fund. The Funds' nominating committees are considering candidates for
the vacancy.
 
                                    TABLE I
                      NOMINEES FOR EACH FUND TO BE ELECTED
                              BY ALL SHAREHOLDERS
 


                                                  FULL COMMON SHARES
                                                  BENEFICIALLY OWNED
                                   YEAR FIRST      SEPTEMBER 1, 1995
    NAME, AGE AND PRINCIPAL         ELECTED       -------------------
 OCCUPATIONS OF NOMINEES AS OF   OR APPOINTED A     THE    ALL NUVEEN
      SEPTEMBER 1, 1995(1)          TRUSTEE       FUNDS(2)  FUNDS(3)
 -----------------------------   --------------   -------- ----------
                                                  
 *Richard J. Franke(64)         1993--All Funds       0      20,719
   Chairman of the Board and
   Trustee of the Funds, The
   John Nuveen Company (since
   March 1992), John Nuveen &
   Co. Incorporated, Nuveen
   Advisory Corp. and Nuveen
   Institutional Advisory
   Corp. (since April 1990);
   Certified Financial
   Planner.
 Lawrence H. Brown(61)          1993--All Funds       0       3,487
   Trustee of the Funds;
   retired in August 1989 as
   Senior Vice President of
   The Northern Trust Company.
 Anne E. Impellizzeri(62)       1994--All Funds       0       2,000
   Trustee of the Funds;
   President and Chief
   Executive Officer of
   Blanton-Peale, Institutes
   of Religion and Health
   (since December 1990);
   prior thereto, Vice
   President of New York City
   Partnership (from 1988 to
   1990) and Vice President of
   Metropolitan Life Insurance
   Company (from 1980 to
   1988).
 Peter R. Sawers(62)            1993--All Funds       0       7,972
   Trustee of the Funds;
   Adjunct Professor of
   Business and Economics,
   University of Dubuque, Iowa
   (since January 1991);
   Adjunct Professor, Lake
   Forest Graduate School of
   Management, Lake Forest,
   Illinois (since January
   1992); prior thereto,
   Executive Director, Towers
   Perrin Australia
   (management consultant);
   Chartered Financial
   Analyst; Certified
   Management Consultant.

 
 
                                       4

 
                                    TABLE II
                      NOMINEES FOR EACH FUND TO BE ELECTED
                          BY HOLDERS OF MUNIPREFERRED
 


                                                         FULL COMMON SHARES
                                                         BENEFICIALLY OWNED
                                                          SEPTEMBER 1, 1995
    NAME, AGE AND PRINCIPAL                              -------------------
 OCCUPATIONS OF NOMINEES AS OF    YEAR FIRST ELECTED       THE    ALL NUVEEN
      SEPTEMBER 1, 1995(1)      OR APPOINTED A TRUSTEE   FUNDS(2)  FUNDS(3)
 -----------------------------  ----------------------   -------- ----------
                                                         
 Margaret K. Rosenheim(69)          1993--All Funds          0       5,115
   Trustee of the Funds; Helen
   Ross Professor of Social
   Welfare Policy, School of
   Social Service
   Administration, University
   of Chicago.
 *Timothy R. Schwertfeger(46)       1994--All Funds          0      90,622
   President and Trustee of
   the Funds (since July
   1994); Executive Vice
   President and Director of
   The John Nuveen Company
   (since March 1992) and John
   Nuveen & Co. Incorporated;
   Director of Nuveen Advisory
   Corp. (since October 1992)
   and Nuveen Institutional
   Advisory Corp. (since
   October 1992).

- -----------
  (*) "Interested person" as defined in the Investment Company Act of 1940, as
amended, by reason of being an officer or director of the Funds' investment
adviser, Nuveen Advisory Corp.
 
  (1) The trustee nominees of the Funds are directors or trustees, as the case
may be, of 21 Nuveen open-end funds and 55 Nuveen closed-end funds.
 
 
  (2) No nominee beneficially owned on September 1, 1995, any Common Shares or
MuniPreferred of the Funds.
 
  (3) The number shown reflects the aggregate number of common shares
beneficially owned by the nominee in all of the funds managed by Nuveen
Advisory Corp. and referred to in note (1) above (excluding money market
funds).
 
  EACH FUND'S BOARD OF TRUSTEES UNANIMOUSLY RECOMMENDS THAT SHAREHOLDERS VOTE
FOR THE ELECTION OF THE NOMINEES FOR TRUSTEE.
 
  The trustees affiliated with John Nuveen & Co. Incorporated ("Nuveen") or
Nuveen Advisory Corp. (the "Adviser") serve without any compensation from the
Funds. Trustees who are not affiliated with Nuveen or the Adviser receive a
$45,000 annual retainer for serving as a director or trustee, as the case may
be, of all funds sponsored by Nuveen and managed by the Adviser and a $1,000
fee per day plus expenses for attendance at all meetings held on a day on which
a regularly scheduled Board meeting is held, a $1,000 fee per day plus expenses
for attendance in person or a $500 fee per day plus expenses for attendance by
telephone at a meeting held on a day on which no regular Board meeting is held,
and a $250 fee per day plus expenses for attendance in person or by telephone
at a meeting of the executive committee. The annual retainer, fees and expenses
are allocated among the funds managed by the Adviser on the basis of relative
net asset sizes. Each Fund has adopted a Directors' Deferred Compensation Plan
 
                                       5

 
pursuant to which a trustee of that Fund may elect to have all or a portion of
the trustee's fee deferred. Trustees may defer fees for any calendar year by
the execution of a Participation Agreement prior to the beginning of the
calendar year during which the trustee wishes to begin deferral.
 
  The tables below show, for each trustee who is not affiliated with Nuveen or
the Adviser, the aggregate compensation paid by each Fund for its fiscal year
ended May 31, 1995 and the total compensation that Nuveen funds accrued for
each trustee during the calendar year 1994, including any interest accrued for
trustees on deferred compensation. The rate of earnings on deferred
compensation is equivalent to the average net earnings rate, computed on a
quarterly basis, on the shares of such Nuveen fund.
 


NAME OF TRUSTEE             AGGREGATE COMPENSATION FROM THE FUNDS
- ---------------          --------------------------------------------
                         CONNECTICUT GEORGIA  MARYLAND  MASSACHUSETTS
                           PREMIUM   PREMIUM PREMIUM(2)    PREMIUM
                         ----------- ------- ---------- -------------
                                                       
Lawrence H. Brown           $287       252      502          276
Anne E. Impellizzeri(1)     $287       252      502          276
Margaret K. Rosenheim       $299       260      526          287
Peter R. Sawers             $287       252      502          276

 


NAME OF TRUSTEE           AGGREGATE COMPENSATION FROM THE FUNDS     TOTAL
- ---------------          --------------------------------------- COMPENSATION
                                   NORTH                         NUVEEN FUNDS
                         MISSOURI CAROLINA  VIRGINIA  WASHINGTON ACCRUED FOR
                         PREMIUM  PREMIUM  PREMIUM(3)  PREMIUM   TRUSTEES(4)
                         -------- -------- ---------- ---------- ------------
                                                            
Lawrence H. Brown          $213     314       453        219        56,500
Anne E. Impellizzeri(1)    $213     314       453        219        48,750
Margaret K. Rosenheim      $218     328       473        224        64,404(5)
Peter R. Sawers            $213     314       453        219        56,000

- -----------
  (1) Anne E. Impellizzeri was appointed a Board Member in April 1994.
 
  (2) Includes $139 for Ms. Impellizzeri and Messrs. Brown and Sawers,
individually, and $144 for Mrs. Rosenheim paid from Nuveen Maryland Premium
Income Municipal Fund 2 for its first two fiscal quarters prior to its merger
into Maryland Premium.
 
  (3) Includes $114 for Ms. Impellizzeri and Messrs. Brown and Sawers,
individually, and $118 for Mrs. Rosenheim paid from Nuveen Virginia Premium
Income Municipal Fund 2 for its first two fiscal quarters prior to its merger
into Virginia Premium.
 
  (4) Includes compensation for service on the boards of 21 Nuveen open-end
funds and 55 Nuveen closed-end funds. Also includes amounts for Nuveen funds
that existed for part of the year, estimated as if the funds had existed for
the entire year.
 
  (5) Includes $1,404 in interest accrued on deferred compensation from prior
years.
 
  Richard J. Franke, Margaret K. Rosenheim and Timothy R. Schwertfeger serve
as members of the executive committee of the Board of Trustees of each Fund.
The executive committee of each Fund, which meets between regular meetings of
the Board of Trustees, is authorized to exercise all of the powers of the
Board of Trustees. The respective executive committees of Connecticut Premium,
Georgia Premium, Massachusetts Premium, Missouri Premium, North Carolina
Premium and Washington Premium held twelve meetings during the
 
                                       6

 
fiscal year ended May 31, 1995. The respective executive committees of Maryland
Premium and Virginia Premium held thirteen meetings during the fiscal year
ended May 31, 1995.
 
  Each Fund's Board of Trustees has an audit committee composed of Lawrence H.
Brown, Anne E. Impellizzeri, Margaret K. Rosenheim and Peter R. Sawers,
trustees who are not "interested persons." The audit committee reviews the work
and any recommendations of the Fund's independent auditors. Based on such
review, it is authorized to make recommendations to the Board of Trustees. The
respective audit committees of the Funds held one meeting during the fiscal
year ended May 31, 1995.
 
  Nomination of those trustees who are not "interested persons" of each Fund is
committed to a nominating committee composed of the trustees who are not
"interested persons" of that Fund. It identifies and recommends individuals to
be nominated for election as non-interested trustees. The respective nominating
committees of the Funds held no meetings during the fiscal year ended May 31,
1995. No policy or procedure has been established as to the recommendation of
trustee nominees by shareholders.
 
  Each Fund's Board of Trustees held five meetings during the fiscal year ended
May 31, 1995. During the last fiscal year, each trustee attended 75% or more of
each Fund's Board of Trustees meetings and the committee meetings (if a member
thereof), except that Mr. Franke was unable to attend certain executive
committee meetings held solely to declare dividends. His attendance at
executive committee meetings that he was scheduled to attend was less than 75%.
 
  Each Fund has the same executive officers. The following table sets forth
information as of September 15, 1995 with respect to each executive officer of
the Funds, other than executive officers who are trustees and reflected above.
Officers of the Funds receive no compensation from the Funds. The term of
office of all officers will expire at the regularly scheduled meeting of the
Board of Trustees of each Fund following the annual meetings of shareholders.
 


                            POSITIONS AND
         NAME         AGE OFFICES WITH FUNDS       PRINCIPAL OCCUPATIONS
         ----         --- ------------------       ---------------------
                                    
 Kathleen M. Flanagan  48   Vice President   Vice President of John Nuveen &
                            (since 1994)       Co. Incorporated.
 J. Thomas Futrell     40   Vice President   Vice President of Nuveen Advisory
                            (since 1993)       Corp. (since February 1991);
                                               prior thereto, Assistant Vice
                                               President of Nuveen Advisory
                                               Corp. (from August 1988 to
                                               February 1991); Chartered
                                               Financial Analyst.
 Steven J. Krupa       38   Vice President   Vice President of Nuveen Advisory
                            (since 1993)       Corp. (since October 1990);
                                               prior thereto, Vice President
                                               of John Nuveen & Co.
                                               Incorporated (from January 1989
                                               to October 1990).
 Anna R. Kucinskis     49   Vice President   Vice President of John Nuveen &
                            (since 1993)       Co. Incorporated.

 
                                       7

 


                               POSITIONS AND
          NAME           AGE OFFICES WITH FUNDS      PRINCIPAL OCCUPATIONS
          ----           --- ------------------      ---------------------
                                       
 Larry W. Martin          44   Vice President   Vice President (since September
                               & Assistant        1993), Assistant Secretary
                               Secretary          and Assistant General Counsel
                               (since 1993)       of John Nuveen & Co.
                                                  Incorporated; Vice President
                                                  (since May 1993) and
                                                  Assistant Secretary of Nuveen
                                                  Advisory Corp.; Vice
                                                  President (since May 1993)
                                                  and Assistant Secretary
                                                  (since January 1992) of
                                                  Nuveen Institutional Advisory
                                                  Corp.; Assistant Secretary
                                                  (since February 1993) of The
                                                  John Nuveen Company; Director
                                                  of Nuveen/Duff & Phelps
                                                  Investment Advisors (since
                                                  January 1995).
 O. Walter Renfftlen      56   Vice President   Vice President and Controller
                               & Controller       of The John Nuveen Company
                               (since 1993)       (since March 1992), John
                                                  Nuveen & Co. Incorporated,
                                                  Nuveen Advisory Corp. and
                                                  Nuveen Institutional Advisory
                                                  Corp.
 Thomas C. Spalding, Jr.  44   Vice President   Vice President of Nuveen
                               (since 1993)       Advisory Corp. (since
                                                  February 1982) and Nuveen
                                                  Institutional Advisory Corp.;
                                                  Chartered Financial Analyst.
 H. William Stabenow      61   Vice President   Vice President and Treasurer of
                               & Treasurer        The John Nuveen Company
                               (since 1993)       (since March 1992), John
                                                  Nuveen & Co. Incorporated,
                                                  Nuveen Advisory Corp. and
                                                  Nuveen Institutional Advisory
                                                  Corp. (since January 1992).
 George P. Thermos        63   Vice President   Vice President of John Nuveen &
                               (since 1993)       Co. Incorporated.
 James J. Wesolowski      45   Vice President   Vice President, General Counsel
                               & Secretary        and Secretary of The John
                               (since 1993)       Nuveen Company (since March
                                                  1992), John Nuveen & Co.
                                                  Incorporated, Nuveen Advisory
                                                  Corp. and Nuveen
                                                  Institutional Advisory Corp.
 Gifford R. Zimmerman     39   Vice President   Vice President (since September
                               & Assistant        1992), Assistant Secretary
                               Secretary          and Assistant General Counsel
                               (since 1993)       of John Nuveen & Co.
                                                  Incorporated; Vice President
                                                  (since May 1993) and
                                                  Assistant Secretary of Nuveen
                                                  Advisory Corp.; Vice
                                                  President (since May 1993)
                                                  and Assistant Secretary
                                                  (since January 1992) of
                                                  Nuveen Institutional Advisory
                                                  Corp.

 
  On September 1, 1995, trustees and executive officers of the Funds as a group
beneficially owned 204,624 common shares of all funds managed by the Adviser
(excluding money market funds) and as a group did not beneficially own any
Common Shares or MuniPreferred of any Fund. As of September 1, 1995, no person
is known to the Funds to have owned beneficially more than five percent of the
Common Shares or MuniPreferred of any Fund.
 
                                       8

 
  Section 30(f) of the Investment Company Act of 1940, as amended (the "1940
Act"), and Section 16(a) of the Securities Exchange Act of 1934, as amended,
require each Fund's officers and trustees, investment adviser, affiliated
persons of the investment adviser and persons who own more than ten percent of
a registered class of the Funds' equity securities to file forms reporting
their affiliation with that Fund and reports of ownership and changes in
ownership of that Fund's shares with the Securities and Exchange Commission
(the "SEC") and the New York Stock Exchange. These persons and entities are
required by SEC regulation to furnish the Funds with copies of all Section
16(a) forms they file. Based on a review of these forms furnished to each Fund,
each Fund believes that during the fiscal year ended May 31, 1995, all Section
16(a) filing requirements applicable to that Fund's officers and trustees,
investment adviser and affiliated persons of the investment adviser were
complied with.
 
                      2. SELECTION OF INDEPENDENT AUDITORS
 
  The members of each Fund's Board of Trustees who are not "interested persons"
of that Fund have unanimously selected Ernst & Young LLP, independent public
accountants, as independent auditors, to audit the books and records of that
Fund for the fiscal year ending May 31, 1996. Ernst & Young LLP has served each
Fund in this capacity since that Fund was organized and has no direct or
indirect financial interest in that Fund except as independent auditors. The
selection of Ernst & Young LLP as independent auditors of each Fund is being
submitted to the shareholders for ratification, which requires the affirmative
vote of a majority of the shares of each Fund present and entitled to vote on
the matter. A representative of Ernst & Young LLP is expected to be present at
the Annual Meetings and will be available to respond to any appropriate
questions raised at the Annual Meetings and to make a statement if he or she
wishes. EACH FUND'S BOARD OF TRUSTEES UNANIMOUSLY RECOMMENDS THAT SHAREHOLDERS
VOTE FOR THE RATIFICATION OF THE SELECTION OF INDEPENDENT AUDITORS.
 
INFORMATION ABOUT THE FUNDS' INVESTMENT ADVISER
 
  The Adviser, located at 333 West Wacker Drive, Chicago, Illinois, serves as
investment adviser and manager for each Fund. The Adviser is a wholly-owned
subsidiary of Nuveen, 333 West Wacker Drive, Chicago, Illinois 60606. Nuveen is
a subsidiary of The John Nuveen Company which in turn is approximately 75%
owned by The St. Paul Companies, Inc. ("St. Paul"). St. Paul is located at 385
Washington Street, St. Paul, Minnesota 55102, and is principally engaged in
providing property-liability insurance through subsidiaries. Nuveen acted as
co-managing underwriter for each Fund in connection with such Fund's public
offering of Common Shares and MuniPreferred.
 
                                       9

 
                             SHAREHOLDER PROPOSALS
 
  To be considered for presentation at the Annual Meeting of Shareholders of
any of the Funds to be held in 1996, a shareholder proposal must be received at
the offices of that Fund, 333 West Wacker Drive, Chicago, Illinois 60606, not
later than June 1, 1996.
 
                                    GENERAL
 
  Management does not intend to present and does not have reason to believe
that any other items of business will be presented at any Fund's Annual
Meeting. However, if other matters are properly presented to the Annual Meeting
for a vote, the proxies will be voted upon such matters in accordance with the
judgment of the persons acting under the proxies.
 
  A list of shareholders entitled to be present and to vote at each Fund's
Annual Meeting will be available at the offices of the Funds, 333 West Wacker
Drive, Chicago, Illinois, for inspection by any shareholder during regular
business hours for ten days prior to the date of that Annual Meeting.
 
  Failure of a quorum to be present at any Annual Meeting will necessitate
adjournment and will subject that Fund to additional expense. The persons named
in the enclosed proxy may also move for an adjournment of any Annual Meeting to
permit further solicitation of proxies with respect to any of the proposals if
they determine that adjournment and further solicitation is reasonable and in
the best interests of the shareholders. Under each Fund's By-Laws, an
adjournment of a meeting requires the affirmative vote of a majority of the
shares present in person or represented by proxy at the meeting.
 
  IF YOU CANNOT BE PRESENT IN PERSON, YOU ARE REQUESTED TO FILL IN, SIGN AND
RETURN THE ENCLOSED PROXY PROMPTLY. NO POSTAGE IS REQUIRED IF MAILED IN THE
UNITED STATES.
 
                                       James J. Wesolowski
                                            Secretary
 
                                                                         NTC1195
 
                                       10

 
 
                                                                    PROXY BALLOT
 
NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND
 
COMMON SHARES
PROXY SOLICITED BY THE BOARD OF TRUSTEES
FOR ANNUAL MEETING OF SHAREHOLDERS
TO BE HELD ON NOVEMBER 16, 1995
 
The undersigned hereby appoints Richard J. Franke, Timothy R. Schwertfeger and
James J. Wesolowski, and each of them, with full power of substitution, Proxies
for the undersigned to represent and vote the common shares of the undersigned
at the Annual Meeting of Shareholders of Nuveen Connecticut Premium Income
Municipal Fund to be held on November 16, 1995, or any adjournment or
adjournments thereof:
 
1. Election of Trustees:
   NOMINEES: Lawrence H. Brown, Richard J. Franke, Anne E. Impellizzeri,
   Peter R. Sawers.
2. Ratification of the selection of Ernst & Young LLP as independent auditors
   for the fiscal year ending May 31, 1996.
3. In their discretion, the Proxies are authorized to vote upon such other
   business as may properly come before the Annual Meeting.

- ------------------------------------------------------------------------------ 
   You are encouraged to specify your choices by marking the appropriate
   boxes ON THE REVERSE SIDE. If you do not mark any boxes, your Proxy
   will be voted in accordance with the Board of Trustees'
   recommendations. Please sign, date and return this Proxy card
   promptly using the enclosed envelope.
- ------------------------------------------------------------------------------ 
 
                                SEE REVERSE SIDE                         NTC1195

                
THE BOARD OF DIRECTORS RECOMMENDS A VOTE FOR ALL NOMINEES AND THE PROPOSAL:
                                  Please mark your votes as in this example. [X]
 
- --------------------------------------------------------------------------------
 
1. ELECTION OF TRUSTEES:(SEE REVERSE FOR NOMINEES)         
   [_] FOR all nominees 
   [_] WITHHOLD authority to vote for all nominees
   [_] WITHHOLD authority to vote for nominees indicated below:

INSTRUCTIONS:
TO GRANT AUTHORITY TO VOTE FOR ALL NOMINEES, MARK THE BOX ON THE LEFT ABOVE OR
DO NOT MARK ANY BOX ABOVE.
TO WITHHOLD AUTHORITY TO VOTE FOR ALL NOMINEES, MARK THE BOX IN THE MIDDLE
ABOVE.
TO WITHHOLD AUTHORITY TO VOTE FOR ANY ONE OR MORE OF THE NOMINEES, MARK THE
BOX ON THE RIGHT ABOVE AND WRITE EACH NOMINEE'S NAME IN THE SPACE PROVIDED.

- --------------------------------

2. RATIFICATION OF THE SELECTION OF ERNST & YOUNG LLP AS INDEPENDENT AUDITORS
   FOR THE FISCAL YEAR ENDING JULY 31, 1996.

3. IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO VOTE UPON SUCH OTHER
   BUSINESS AS MAY PROPERLY COME BEFORE THE ANNUAL MEETING.

   FOR [_]    AGAINST [_]   ABSTAIN [_] 

- --------------------------------------------------------------------------------

THE SHARES TO WHICH THIS PROXY RELATES WILL BE VOTED AS SPECIFIED. IF NO
SPECIFICATION IS MADE, SUCH SHARES WILL BE VOTED FOR THE ELECTION OF TRUSTEES
AND FOR THE PROPOSAL SET FORTH ON THIS PROXY.
 
 
 Please be sure to sign and date this Proxy.


- -----------------------------------------------------------
 
 Shareholder sign here _________________________ Date _____
 
 
 Co-owner sign here ____________________________ Date _____

- -----------------------------------------------------------
  
NOTE: Please sign exactly as your name appears on this
Proxy. If signing for estates, trusts or corporations, title
or capacity should be stated. If shares are held jointly,
each holder should sign.
 
[_] BK NTC1195                                       NTC1195

 
 
                                                                    PROXY BALLOT
 
NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND
 
MUNICIPAL AUCTION RATE CUMULATIVE PREFERRED SHARES, SERIES TH
PROXY SOLICITED BY THE BOARD OF TRUSTEES
FOR ANNUAL MEETING OF SHAREHOLDERS
TO BE HELD ON NOVEMBER 16, 1995
 
The undersigned hereby appoints Richard J. Franke, Timothy R. Schwertfeger and
James J. Wesolowski, and each of them, with full power of substitution, Proxies
for the undersigned to represent and vote the shares of Municipal Auction Rate
Cumulative Preferred Shares, Series TH, of the undersigned at the Annual
Meeting of Shareholders of Nuveen Connecticut Premium Income Municipal Fund to
be held on November 16, 1995, or any adjournment or adjournments thereof:
 
1. Election of Trustees:
   NOMINEES--BY ALL SHAREHOLDERS: Lawrence H. Brown, Richard J. Franke, Anne E.
             Impellizzeri, Peter R. Sawers.
   NOMINEES--BY HOLDERS OF MUNICIPAL AUCTION RATE CUMULATIVE PREFERRED SHARES
             ONLY: Margaret K. Rosenheim, Timothy R. Schwertfeger.
2. Ratification of the selection of Ernst & Young LLP as independent auditors
   for the fiscal year ending May 31, 1996.
3. In their discretion, the Proxies are authorized to vote upon such other
   business as may properly come before the Annual Meeting.
 
- -------------------------------------------------------------------------------
   You are encouraged to specify your choices by marking the appropriate
   boxes ON THE REVERSE SIDE. If you do not mark any boxes, your Proxy
   will be voted in accordance with the Board of Trustees'
   recommendations. Please sign, date and return this Proxy card
   promptly using the enclosed envelope.
- -------------------------------------------------------------------------------
 
                                SEE REVERSE SIDE                        NTC1195P

                
THE BOARD OF DIRECTORS RECOMMENDS A VOTE FOR ALL NOMINEES AND THE PROPOSAL:
                                  Please mark your votes as in this example. [X]
 
- --------------------------------------------------------------------------------
 
1. ELECTION OF TRUSTEES:(SEE REVERSE FOR NOMINEES)         
   [_] FOR all nominees 
   [_] WITHHOLD authority to vote for all nominees
   [_] WITHHOLD authority to vote for nominees indicated below:
       

INSTRUCTIONS:
TO GRANT AUTHORITY TO VOTE FOR ALL NOMINEES, MARK THE BOX ON THE LEFT ABOVE OR
DO NOT MARK ANY BOX ABOVE.
TO WITHHOLD AUTHORITY TO VOTE FOR ALL NOMINEES, MARK THE BOX IN THE MIDDLE
ABOVE.
TO WITHHOLD AUTHORITY TO VOTE FOR ANY ONE OR MORE OF THE NOMINEES, MARK THE
BOX ON THE RIGHT ABOVE AND WRITE EACH NOMINEE'S NAME IN THE SPACE PROVIDED.

- --------------------------------

2. RATIFICATION OF THE SELECTION OF ERNST & YOUNG LLP AS INDEPENDENT AUDITORS
   FOR THE FISCAL YEAR ENDING JULY 31, 1996.

3. IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO VOTE UPON SUCH OTHER
   BUSINESS AS MAY PROPERLY COME BEFORE THE ANNUAL MEETING.

   FOR [_]    AGAINST [_]   ABSTAIN [_] 

- --------------------------------------------------------------------------------

THE SHARES TO WHICH THIS PROXY RELATES WILL BE VOTED AS SPECIFIED. IF NO
SPECIFICATION IS MADE, SUCH SHARES WILL BE VOTED FOR THE ELECTION OF TRUSTEES
AND FOR THE PROPOSAL SET FORTH ON THIS PROXY.
 
 
 Please be sure to sign and date this Proxy.


- -----------------------------------------------------------
 
 Shareholder sign here _________________________ Date _____
 
 
 Co-owner sign here ____________________________ Date _____

- -----------------------------------------------------------
  
NOTE: Please sign exactly as your name appears on this
Proxy. If signing for estates, trusts or corporations, title
or capacity should be stated. If shares are held jointly,
each holder should sign.
 
[_] BK NTC1195                                     NTC1195P