Notwithstanding any other provision of the general statutes, any special act or home rule charter, any special election held to fill a vacancy in a district office or in a municipal office in a political subdivision, including the municipal office of state senator or state representative, shall be held in the district or political subdivision which was represented by the person who vacated such office, and the voting districts used for purposes of such special election, including the nomination of candidates to run in such election, shall conform to the boundaries of such district or political subdivision.
Conn. Gen. Stat. § 9-169e
(Nov. Sp. Sess. P.A. 81-3, S. 3, 5.)
See part III (Secs. 9-211 to 9-224, inclusive) re procedure for filling vacancies in specific offices.