Conn. Gen. Stat. § 9-221

(b) When under the provisions of any general statute, special act or charter, it is required that a vacancy in any municipal office be filled at the next municipal election, such provisions shall not apply to any such vacancy which occurs after the deadline for the nomination of candidates specified in section 9-452 and any such vacancy thereafter occurring may be filled until such election, by the official or officials authorized to fill such vacancy, by the appointment of a qualified person to serve until such election and shall forthwith be filled after such election by the official or officials so authorized who are serving after such election by the appointment of a qualified person, provided the period of thirty days set forth in section 7-107 shall not begin with respect to such vacancy until the day after the day of such election and provided, if any portion of the term in which such vacancy occurred remains unexpired after the second municipal election to be held in such municipality after the time of its occurrence, it shall be filled at such second municipal election, except as herein provided.

(c) When under the provisions of any general statute, special act or charter, it is required that a vacancy in any municipal office be filled at the next municipal election, and such a vacancy occurs after the day before the time specified in section 9-391 for the parties to endorse candidates to run in a primary for nomination to an office and prior to the deadline for the nomination of candidates specified in section 9-452 , nomination of a candidate for such vacancy may be made only by a major or minor party, as defined in section 9-372 , entitled to a place on the ballot with respect to such office under section 9-379 and shall be made by the appointment of a nominee by the town committee of any such party in such municipality, which nomination shall be certified to the clerk of such municipality by the chairman and secretary of such town committee not later than four o'clock p.m. of the fifth day following the deadline for the nomination of candidates specified in section 9-452 , except that when such date is a Saturday, Sunday or legal holiday, such certification shall be made not later than four o'clock p.m. of the next succeeding business day. The municipal clerk shall include the name of any such nominee in the list of candidates of each party for the municipal offices to be filled at such election in accordance with section 9-461 . Upon the occurrence of any such vacancy, such municipal clerk shall forthwith notify in writing the chairman or secretary of the town committee of any such party in such municipality of its occurrence.

Cited. 41 CS 267.