Conn. Gen. Stat. § 9-422

Any provision of sections 9-382 to 9-450 , inclusive, to the contrary notwithstanding, no primary shall be held for nomination by a party to the office of justice of the peace unless candidacies for such nomination numbering at least a bare majority of the number of justices of the peace to be nominated by such party are filed in conformity with the provisions of sections 9-400 to 9-414 , inclusive, by persons other than party-endorsed candidates.