Conn. Gen. Stat. § 9-52: Discretionary enrollment sessions.

The registrars of voters in each municipality may hold additional discretionary enrollment sessions for the purpose of making an enrollment of the electors who are entitled to vote in any primary or caucus in such municipality at such other times as all such registrars in such municipality deem necessary; but no such session shall be held on the day when a caucus or primary is held or during the fourteen days preceding a primary or the day before a caucus.