New York Consolidated Laws, Civil Practice Law and Rules - CVP § 410. Trial

If triable issues of fact are raised they shall be tried forthwith and the court shall make a final determination thereon.  If issues are triable of right by jury, the court shall give the parties an opportunity to demand a jury trial of such issues.  Failure to make such demand within the time limited by the court, or, if no such time is limited, before trial begins, shall be deemed a waiver of the right to trial by jury.