N.Y. Gen. Mun. Law § 87
Boards of estimate and apportionment, common councils, boards of aldermen, boards of supervisors, town boards, boards of trustees of villages and all other boards or officers of counties, cities, towns and villages, authorized to appropriate and to raise money by taxation and to make payments therefrom, are hereby authorized, in their discretion, to appropriate and to raise money by taxation and to make payments from said moneys, and from any moneys received from any other source and properly applicable thereto, to charitable, eleemosynary, correctional and reformatory institutions wholly or partly under private control, for the care, support and maintenance of their incarcerated individuals and out-patients, of the moneys which are or may be appropriated therefor; such payments to be made only for such incarcerated individuals as are received and retained therein pursuant to regulations established by the state department of social services or other state department having the power of inspection thereof. In the absence within the state of adequate facilities conveniently accessible, payments for the support, care and maintenance of incarcerated individuals and out-patients may be made to institutions, wholly or partly under private control, of a charitable or eleemosynary character, located without the state, which institutions if located within the state would be subject to the visitation, inspection and supervision of the department of social services. However, such payments may be made only to institutions conducted in conformity with the regulations of such department.
N.Y. Gen. Mun. Law § 87