Conn. Gen. Stat. § 9-386
If a vote taken under sections 9-382 to 9-450, inclusive, on the selection of any party-endorsed candidate for state or district office results in a tie, such tie vote shall be dissolved in the manner prescribed in the applicable state or district rules of the party selecting such candidate; provided, if said party rules are silent or permit the tie vote to remain, a tie may be declared by the chairman or the presiding officer and there shall be no party endorsement. In such case of no party endorsement, statements may be filed under section 9-400, by or on behalf of any qualified person whose name appears upon the last-completed enrollment list of such party and who has received at least fifteen per cent of the votes of the convention delegates present and voting on any roll-call vote taken on the proposed endorsement of a candidate for such state or district office. In such event, if within the time specified in section 9-400, a candidacy for nomination to such state or district office is filed in conformity with the provisions of sections 9-400 to 9-414, inclusive, by not more than one person, no primary shall be held by such party for such office and the person filing such candidacy shall be deemed to have been lawfully chosen as the nominee of such party for such office; but if such candidacies are so filed by two or more persons, a primary shall be held as provided in section 9-415.
Conn. Gen. Stat. § 9-386
(November, 1955, S. N63; 1957, P.A. 518, S. 10; 1958 Rev., S. 9-90; 1963, P.A. 17, S. 14; 1967, P.A. 904, S. 1; P.A. 79-616, S. 10; P.A. 93-342, S. 1.)