Conn. Gen. Stat. § 9-382: Party-endorsed candidates; state or district office.

The state or district convention, as the case may be, shall, in a manner conforming with applicable law and with the rules of the party calling such convention, choose a candidate for nomination to each of the state or district offices, as the case may be. No such convention shall choose more than one candidate for nomination to any such office. Candidates so chosen shall run in the primary of such party as party-endorsed candidates, except as provided in section 9-416.