N.Y. Real Prop. Tax Law § 1218
A final determination of the state board of real property tax services relating to state equalization rates may be reviewed by commencing an action in the appellate division of the supreme court in the manner provided by article seventy-eight of the civil practice law and rules upon application of the county, city, town or village for which the rate or rates were established. The standard of review in such a proceeding shall be as specified in subdivision four of section seventy-eight hundred three of the civil practice law and rules. Whenever a final order is issued in such a proceeding directing a revised state equalization rate, any county, village or school district that used the former rate in the apportionment of taxes must, upon receipt of such final order, recalculate the levy that used such former rate and credit or debit as appropriate its constituent municipalities in its next levy. Any special franchise assessments that were established using the former rate must, upon receipt of such final order, be revised by the state board in accordance with the new rate, and, if taxes have already been levied upon such assessments, the affected special franchise owners shall either automatically receive a refund if there is a decrease or be taxed on an increase in the next levy in the manner provided for omitted parcels in title three of article five of this chapter.
N.Y. Real Prop. Tax. Law § 1218