N.Y. Gen. City Law § 21-B
If any joint indebtedness described in title one-A of article two of the local finance law is allocated and apportioned, or is excluded, under or pursuant to such title or any other provision of law for the purpose of determining the debt-contracting power of a county, city, town, village or school district, such allocation and apportionment, or exclusion, shall not limit the amount to be raised in any city outside the limitations applicable to cities set forth in section ten of article eight of the constitution to provide for the interest on and the principal of any greater proportionate share of such debt service which the city has agreed or is required to provide. The total of the amounts which may be so raised by all participating public corporations outside any limitation imposed by or pursuant to section ten of article eight of the constitution to provide for their respective portions of any payment of principal or of interest on joint indebtedness shall not exceed the full amount required to be provided by all of such participants to make any such payment.
N.Y. Gen. City Law § 21-B