N.Y. Public Authorities Law § 1277
1. a. The operation, maintenance and use of passenger stations shall be public purposes of the city of New York and the counties within the district. The total cost to the authority and each of its subsidiary corporations of operation, maintenance and use of each passenger station within the district serviced by one or more railroad facilities of the authority or of such subsidiary corporation, including the buildings, appurtenances, platforms, lands and approaches incidental or adjacent thereto, shall be borne by the city of New York if such station is located in such city or, if not located in such city, by such county within the district in which such station is located. On or before June first of each year, the authority shall, in accordance with the method specified herein, determine and certify to the city of New York and to each county within the district the respective allocation of costs related to the operation, maintenance and use of passenger stations within such city and each such other county, for the twelve month period ending the preceding March thirty-first.