N.Y. Elec. Law § 12-200

§ 12-200. United States senators; election of. At the general election\nnext preceding the expiration of the term of office of a United States\nsenator from this state, a United States senator shall be elected by the\npeople for a full term of six years. Elections to fill a vacancy for an\nunexpired term shall be held as provided in the public officers law.\n