Conn. Gen. Stat. § 9-431

(b) Any such person offering to vote and being challenged as to his identity or residence shall, before he votes, prove by the testimony, under oath, of at least one other elector qualified to vote in such primary or by such other evidence acceptable to the moderator either of the following which are applicable: (1) His identity with the person on whose name he offers to vote or (2) his bona fide residence in the municipality or political subdivision holding the primary, as the case may be. The rules of each party in each municipality shall prescribe whether members of the town committee shall be elected from the municipality at large, in which case any person on the last-completed enrollment list of such party in such municipality shall be eligible to vote in a primary for the election of such committee members, or whether such committee members shall be elected from political subdivisions of such municipality, in which case only persons on the last-completed list of such party in such a political subdivision shall be eligible to vote in a primary for the election of such committee members from such political subdivision; provided no town committee in any municipality shall be elected both at large and from political subdivisions.

(c) Any citizen who has not yet attained the age of eighteen years but who will have attained the age of eighteen years on or before the day of a regular election, and who: (1) Is otherwise qualified to be an elector, and (2) has applied for admission as an elector, may vote at a primary of a party held for such regular election pursuant to subsections (a) and (b) of this section.