N.Y. C.P.L.R. 8403

§ 8403. Taxation without notice. Costs may also be taxed without\nnotice. A party who has taxed costs without notice shall immediately\nserve a copy of the bill of costs upon each party who is entitled to\nnotice under section 8402. Within five days after such service, any\nsuch party may serve notice of retaxation of costs upon five days'\nnotice to the party who has taxed the costs, specifying the item as to\nwhich retaxation is sought.\n