N.Y. High. Law § 131-E
The board shall provide for the care, maintenance, preservation and repair of any draw or other bridge intersecting the boundary line of counties or towns, which bridge is by law a joint charge on such counties or towns, or on the towns in which it is situated; and to severally apportion, as it may deem equitable, the expenses thereof on the towns respectively liable therefor, or on the respective counties when liable; but when such bridge shall span any portion of the navigable tide-waters of this state, forming, at the point of crossing, the boundary line between two counties, such expense shall be a joint and equal charge upon the two counties in which the bridge is situated, and the board of supervisors in each of such counties shall apportion such expense among the several towns and cities in their respective counties, or upon any or either of such towns and cities, as in their judgment may seem proper; and if there be in either of said counties, a city, the boundaries of which are the same as the boundaries of the county, then it shall be the duty of the common council of such city, to perform the duty hereby imposed upon the boards of supervisors; but no town or city not immediately adjacent to such waters at the points spanned by said bridge shall be liable for a larger proportion of such expense than the taxable property of such town or city bears to the whole amount of taxable property of such county. The board of supervisors of such counties or, in any city embracing the entire county and having no board of supervisors, the common council, shall have full control of such bridges. No such bridge shall be constructed unless the board of supervisors in each of such counties, and the common council of the city whose boundaries are the same as the boundary of the other county adjacent to such waters, shall first by resolution determine that such bridge is necessary for public convenience. Whenever any bridge now spanning any such navigable tide-waters or hereafter erected across any such navigable tide-waters, shall be condemned by the United States authorities as an obstruction to navigation, and shall be ordered removed, the county and city authorities having charge of such bridge, if they shall determine that such bridge shall be rebuilt, shall, as soon as practicable after such determination, cause plans to be prepared for the erection of the new bridge and the removal of any bridge so condemned as aforesaid, and within a reasonable time after the approval of any such plans by the United States authorities, the proper officers shall proceed with the construction of said new bridge. In case of any unreasonable delay on the part of the officer or officers charged with the duty of construction of such new bridge, such duty may be enforced by mandamus upon the application of any citizen interested in its performance.
N.Y. High. Law § 131-E