Conn. Gen. Stat. § 9-211a

Notwithstanding the provisions of section 9-211 , in the event that among the states there are fifty or more vacancies in the office of senator in Congress at any single point in time and one of such vacancies is from Connecticut, the Governor is empowered to fill such vacancy by appointment as herein provided. If such vacancy occurs one hundred fifty or more days prior to a state election, the appointee shall serve until the third day of January following such election, and at such election there shall be elected a senator in Congress to serve for the remaining portion, if any, of the term vacated. If such vacancy occurs within less than one hundred fifty days of a state election and the term vacated does not expire on the third day of January following such election, the appointee shall serve until the third day of January following the next such election but one, and at such next election but one there shall be elected a senator in Congress to serve for the remaining portion, if any, of the term vacated. If such vacancy occurs within less than one hundred fifty days of a state election and the term vacated expires on the third day of January following, the appointee shall serve until such third day of January.