Conn. Gen. Stat. § 9-426

(b) If candidacies have been filed by only one group of persons other than party-endorsed candidates for election to a town committee, and the candidates whose candidacies have been so filed thereafter, but prior to the opening of the polls at such primary, die, withdraw their names from nomination or for any reason become disqualified to hold the positions for which they are candidates, so as to render the number of candidacies so filed less than twenty-five per cent of the number of town committee members to be elected by such party either in the municipality or in the political subdivision, as the case may be, no primary shall be held for those positions and the party-endorsed candidates for such positions shall be deemed to have been lawfully chosen in the same manner and to the same extent as is provided in sections 9-382 to 9-450 , inclusive, in the case where no candidacies other than party-endorsed candidacies have been filed.

(c) If any person on a slate, prior to the commencement of the period of early voting at such primary, dies, withdraws his name from nomination or for any reason becomes disqualified to hold the position for which he is a candidate, such partial slate shall appear on the ballot at the primary and, if such partial slate wins, then the remaining members may fill the vacancy. If only one such slate other than a slate of party-endorsed candidates has been filed for election and prior to the commencement of the period of early voting at such primary each of the persons on such slate dies, withdraws or becomes disqualified, no primary shall be held for those positions and the party-endorsed candidates for those positions shall be deemed to have been lawfully chosen in the same manner and to the same extent as is provided in sections 9-382 to 9-450 , inclusive, in the case where no candidacies other than party-endorsed candidacies have been filed.