N.Y. C.P.L.R. 4103

§ 4103. Issues triable by a jury revealed at trial; demand and waiver\nof trial by jury. When it appears in the course of a trial by the court\nthat the relief required, although not originally demanded by a party,\nentitles the adverse party to a trial by jury of certain issues of fact,\nthe court shall give the adverse party an opportunity to demand a jury\ntrial of such issues. Failure to make such demand within the time\nlimited by the court shall be deemed a waiver of the right to trial by\njury. Upon such demand, the court shall order a jury trial of any issues\nof fact which are required to be tried by jury.\n