New York Consolidated Laws, Election Law - ELN § 6-160. Primaries

1. If more candidates are designated for the nomination of a party for an office to be filled by the voters of the entire state than there are vacancies, the nomination or nominations of the party shall be made at the primary election at which other candidates for public office are nominated and the candidate or candidates receiving the most votes shall be the nominees of the party.

2. All persons designated for uncontested offices or positions at a primary election shall be deemed nominated or elected thereto, as the case may be, without balloting.