N.Y. Real Prop. Tax Law § 1514
Notwithstanding the provisions of any general or special law to the contrary, in the county of Westchester the common council, board of aldermen, commission or other legislative body of any city by whatever name called may by resolution or ordinance authorize the collecting officer in such city to accept from any taxpayer at any time partial payments for or on account of taxes, special ad valorem levies and special assessments or on account of any tax liens owned and held by such city in such amount or manner and apply such payments on account thereof in such manner as may be prescribed in such resolution or ordinance. Notwithstanding the provisions of any general or special law to the contrary, such resolution or ordinance may provide that if any installment subsequent to the first installment is paid in the month in which it becomes due, the penalty accrued against such installment may be reduced; provided, however, that such penalty shall not be reduced below the rate of two per cent, through the month in which such installment is due, but if not paid in the month in which such subsequent installment is due, penalties subsequent to that month shall be as presently defined in existing law. No installment payment provided for under this section shall be due later than one month prior to the date upon which the assessment roll on which the tax is levied is closed and succeeded by a new roll. After receiving any such partial payment, interest and penalties shall be charged against the unpaid balance only. The acceptance of a partial payment shall be deemed not to affect any rights and powers of such city in any general or special act including charter or local laws, but such rights and powers shall remain in full force and effect to enforce collection of the unpaid balance together with interest, penalties and other lawful charges thereon.
N.Y. Real Prop. Tax. Law § 1514