N.Y. Second Class Cities Law § 206
The amount of any judgment recovered against the city and payable by it, remaining unpaid, with the interest due thereon, in case the time to appeal therefrom has expired and no appeal has been taken, or a certificate of no appeal therefrom has been given by the corporation counsel, or in case such judgment is finally affirmed, or an appeal taken and the execution thereon shall not be stayed, shall be reported to the common council immediately after the same shall have become payable, as aforesaid; and the amount thereof shall be included in the next city tax budget. Such judgments shall be paid in the order of their recovery out of the moneys first paid into the city treasury on account of the annual taxes or, prior thereto, out of the proceeds of tax anticipation notes issued in anticipation of the collection of such taxes or out of the proceeds of budget notes. If, however, there be any moneys in the treasury to the credit of any fund derived from city revenues, other than taxation, in excess of the estimated revenues from such source, and not otherwise appropriated, sufficient to satisfy judgments against the city, the comptroller shall issue warrants for the payment of such judgments out of said funds in the order of their recovery. Until the moneys applicable to the payment of a judgment have been raised and paid into the city treasury and payment of the judgment has been refused, no execution shall issue against the city unless the amount of such judgment shall not have been included in the tax budget.
N.Y. Second Class Cities Law § 206