Conn. Gen. Stat. § 9-471: Notice of primary.

Forthwith upon determination of the order of candidates on the ballot, the secretary shall send a notice of primary for each party to each town clerk. Such notice shall include the names of the candidates in the order so determined and their addresses. Such notice shall conform, as nearly as may be, to the provisions of section 9-433 concerning notice of primary for nomination to a state office. The town clerk shall, forthwith upon receipt of such notice, cause it to be published in the manner provided in said section.