N.Y. HAY Law § 237

§ 237. When town or county expense. The towns of this state, except as\notherwise herein provided, shall be liable to pay the expenses for the\nconstruction and repair of its public or free bridges constructed over\nstreams or other waters within their bounds, and their just and\nequitable share of such expenses when so constructed over streams or\nother waters upon their boundaries, except between the counties of\nWestchester and New York; and when such bridges are constructed over\nstreams or other waters forming the boundary line of towns, either in\nthe same or adjoining counties, such towns shall be jointly liable to\npay such expenses. When such bridges are constructed over streams or\nother waters forming the boundary line between a city of the third class\nand a town, such city and town shall be liable each to pay its just and\nequitable share of the expenses for the construction, maintenance and\nrepair of such bridges. Except as otherwise provided by law, a city of\nthe third class shall be deemed a town for the purposes of this article.\nEach of the counties of this state shall also be liable to pay for the\nconstruction, care, maintenance, preservation and repair of public\nbridges lawfully constructed over streams or other waters forming its\nboundary line, not less than one-sixth part of the expense of\nconstruction, care, maintenance, preservation and repair, and, except in\na county containing a portion of the Adirondack park, the whole of such\nexpenses of public bridges lawfully constructed or to be constructed\nover streams, or waterways, intersecting county roads.\n