N.Y. Public Housing Law § 31

§ 31. Scope of authority's jurisdiction. The territorial jurisdiction\nof an authority established for a city or village shall be coterminous\nwith the territorial limits of such city or village, and the territorial\njurisdiction of an authority established for a town shall include all\nsuch town, except that such territorial jurisdiction shall not include\nany territory that lies within the boundaries of any village, whether\nsuch village has or has not established an authority. The members of\nsuch town authority shall if they consent and when authorized by\nresolutions of the town board and the village board, act as the\nauthority in and for said village, the same as if it had been created\nespecially for said village.\n