N.Y. Elec. Law § 6-116
A party nomination of a candidate for election to fill a vacancy in an elective office required to be filled at the next general election, occurring after seven days before the last day for circulating designating petitions or after the holding of the meeting or convention to nominate or designate candidates for such, shall be made, after the day of the primary election, by a majority vote of a quorum of the state committee if the vacancy occurs in an office to be filled by all voters of the state, and otherwise by a majority vote of a quorum of the members of a county committee or committees last elected in the political subdivision in which such vacancy is to be filled, or by a majority of such other committee as the rules of the party may provide. A certificate of nomination shall be filed as provided for herein.
N.Y. Elec.Law § 6-116