Conn. Gen. Stat. § 9-168a

(b) Any provision of the general statutes to the contrary notwithstanding, in any municipality in which, at any election or primary, as a result of the assembly, senatorial or congressional district lines in effect, there is a voting district with less than one thousand five hundred electors who vote for a combination of officers that no other electors of the town vote for, the registrars of voters may either provide a suitable polling place therein or may, in lieu thereof, provide separate voting tabulators in the polling place of another voting district in said municipality for use by such electors. If the registrars of voters provide separate voting tabulators in the polling place of another voting district, they shall determine which polling place officials are necessary for the district containing less than one thousand five hundred electors and shall provide the procedure to ensure that the electors use the proper voting tabulators, which procedure may include the registrars of voters prescribing and providing receipts.

(c) In any election or primary where electors in more than one voting district vote in the same building and vote for all the same officers, and the law does not require separate returns, the registrars of voters may combine the voting districts and polling places into one voting district and polling place, with or without integrating the voting districts on the check lists used at the election or primary. The registrars of voters shall file a statement of their action with the town clerk before the election or primary and the town clerk shall label the polling place return form to show which districts are combined on such return.