Conn. Gen. Stat. § 9-378: Nominations without party designation excepted.

In any municipality which, under the provisions of a special act, nominates one or more candidates for municipal office without party designation by nominating petitions or in nonpartisan primaries in addition to the nomination of one or more candidates for such office under party designation, the provisions of this chapter shall apply only to the nomination of such candidates for election therein as are nominated and voted upon under party designation.