N.Y. C.P.L.R. 8102

§ 8102. Limitation of costs where action brought in higher court. A\nplaintiff is not entitled to costs:\n 1. in an action brought in the supreme court in a county within the\ncity of New York which could have been brought, except for the amount\nclaimed, in the civil court of the city of New York, unless he shall\nrecover six thousand dollars or more; or,\n 2. in an action brought in the supreme court in a county not within\nthe city of New York which could have been brought, except for the\namount claimed, in any court of limited monetary jurisdiction in the\ncounty, unless he shall recover five hundred dollars or more; or,\n 3. in an action brought in the county court which could have been\nbrought, except for the amount claimed, in any court of lesser monetary\njurisdiction in the county, unless he shall recover two hundred fifty\ndollars or more.\n