Conn. Gen. Stat. § 9-429: Cancellation of primary for office or town committee when vacancies in candidacies result in no contest.

(a) If, prior to the opening of the polls at a primary for election of town committee members, such a number of candidates have died, withdrawn their names or become ineligible, and have not been replaced as permitted in sections 9-426 and 9-428, as to render the total number of candidates for such position no greater than the number to be elected to such positions, the primary shall not be held, and each of the party-endorsed and other candidates shall be deemed to have been lawfully elected to such positions.

(b) If, prior to the commencement of the period of early voting at a primary for nomination to an office, such a number of candidates have died, withdrawn their names or become ineligible, and have not been replaced as permitted in sections 9-426 and 9-428, as to render the total number of candidates for such office no greater than the number to be nominated to such office, the primary shall not be held, and each of the party-endorsed and other candidates shall be deemed to have been lawfully nominated to such office.