N.Y. Elec. Law § 6-152

§ 6-152. Vacancies caused by death or disqualification and unfilled at\ntime of primary election. If a vacancy shall occur in a designation of a\ncandidate for nomination or election at a primary election, caused by\nthe death or disqualification of a candidate subsequent to noon of the\nseventh day before the primary election and prior to the closing of the\npolls, such vacancy shall not be filled and the votes cast for such\ndeceased or disqualified candidate shall be canvassed and counted, and,\nif he shall receive a plurality of the votes cast, another candidate may\nthereafter be nominated or the vacancy filled as provided by law or the\nrules of the party.\n