Conn. Gen. Stat. § 9-23a
When person admitted as an elector permitted to vote in primary. Exception.
(b) An applicant for admission or enrollment under section 9-26 shall be entitled to vote in a primary if he files his application for admission or enrollment with the town clerk before the day of the primary and is otherwise eligible to vote in the primary.
See Sec. 9-57 re application for enrollment by new elector at time of admission and attachment of party privileges.