N.Y. Priv. Hous. Fin. Law § 556
Notwithstanding the provisions of section fifty-two, subdivisionsthree and four of the public housing law, or of sections thirty-three or ninety-three of this chapter, the real property in a project sold or leased as provided in this article, when the transfer thereunder becomes effective, shall be exempt from local and municipal taxes, other than assessments for local improvements, only to such extent as may be granted by the local legislative body of any municipality in which such project is located; provided, however, that any company to which such project is so sold or leased shall pay, with respect to each such project, local and municipal taxes in amounts not less than the sum or sums which the authority would be obligated to pay to the municipality had it not sold or leased the project to such company. The tax exemption shall operate and continue (1) so long as capital loans of the company to which such project shall have been sold or leased are outstanding, or in case of lease, so long as obligations of the municipality or authority to the government granting financial assistance to the municipality or authority with respect to the project so leased shall continue and (2) until and unless the project shall be repossessed by the authority or municipality. Any project that received a tax exemption under this section may, upon the expiration of the tax exemption period, be granted an additional tax exemption period of up to fifty years, or until such time as the project is no longer operated under the restrictions and for the purposes set forth in this article, whichever is sooner.
N.Y. Priv. Hous. Fin. Law § 556