N.Y. Uniform Just. Ct. Act § 214
In a case brought in the supreme court or county court of Westchester county where money damages only are sought and classification, pretrial or other appropriate procedures in either of said courts or the demand for relief have determined that the potential recovery, assuming liability, in an action or proceeding or counterclaim therein will not exceed the sum of five thousand dollars, exclusive of interest and costs, if such action or proceeding is transferred to a town or village court in the county of Westchester having jurisdiction of the parties under section two hundred thirteen of this act, pursuant to section nineteen of article six of the state constitution, the verdict or judgment of such justice court shall not be subject to the limitation of monetary jurisdiction specified elsewhere in this article for such court, but shall be subject instead to a monetary jurisdiction not to exceed five thousand dollars, exclusive of interest and costs. Alternatively, for purposes of this section only, in the furtherance of the interests of justice, such transfer may be made (a) to a justice court in a municipality adjacent to a municipality designated in section two hundred thirteen of this act or to a justice court in a municipality adjacent to a city in Westchester county whose court would otherwise have had jurisdiction by the calendar justice of the supreme court or judge of the county court; or (b) to any justice court in the county of Westchester by the administrative judge of the ninth judicial district. Costs incurred by local municipalities in administering their courts as a result of the application of this section shall be a charge against the county of Westchester within the amounts appropriated by the county therefor and subject to reasonable rules and regulations thereof by the county.
N.Y. Uniform Justice Court § 214