Conn. Gen. Stat. § 9-416: No-contest nominations; state or district office.

If (1) at a state or district convention no person other than a party-endorsed candidate has received at least fifteen per cent of the votes of the delegates present and voting on any roll-call vote taken on the endorsement or proposed endorsement of a candidate for a state or district office, and (2) within the time specified in section 9-400, no candidacy for nomination by a political party to a state or district office has been filed by or on behalf of a person other than a party-endorsed candidate in conformity with the provisions of section 9-400, no primary shall be held by such party for such office and the party-endorsed candidate for such office shall be deemed to have been lawfully chosen as the nominee of such party for such office.