A denial of costs in an action to a party in whose favor the judgment is entered, an award of costs in an action to a party against whom the judgment is entered, an award of separate costs in an action to one or more parties, or an apportionment of costs among several parties, shall be made in the direction of the court for judgment, or in the report or decision upon which judgment is entered, or, upon motion of the party to be benefited thereby, by an order of the judge or referee who presided at the trial. The decision on a motion shall specify the amount of costs awarded upon the motion, if any, and each party to whom they are awarded. The decision on appeal shall specify the disposition made in regard to costs.
New York Legal Code