Conn. Gen. Stat. § 9-418: Failure of party to endorse; municipal office.

(a) If within the time specified in section 9-391, a party has failed, with respect to the office of state senator or state representative, to certify to the Secretary of the State, or with respect to any other municipal office to be filled, to certify to the clerk of the municipality, the name of any person as a party-endorsed candidate, and if within the time specified in section 9-405, a candidacy for nomination to such 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.

(b) If within the time specified in section 9-391, a party has failed, with respect to any municipal office to be filled by two or more persons, to certify to the clerk of the municipality names of persons as party-endorsed candidates equal in number to the number of persons to be nominated to such office, and if within the time specified in section 9-405, a candidacy or candidacies for nomination to such office are filed in conformity with the provisions of sections 9-400 to 9-414, inclusive, by a number of persons not more than the number for which the party has failed to certify names, no primary shall be held by such party for such office, and each of the party-endorsed candidates and each of the persons filing such candidacies shall be deemed to have been lawfully chosen as the nominees of such party for such office.