N.Y. Uniform District Court Act Law § 213

§ 213. Jurisdiction of justices of the peace. The court shall have:\n (a) concurrently, the jurisdiction of the justices of the peace of\nsuch towns of the county as comprise the district court, and\n (b) in any such town wherein there is no justice of the peace, the\njurisdiction such justice would have if there were such office and\nofficer.\n