N.Y. CCA Law § 1303

§ 1303. Jury trial; how obtained; jury fee. (a) Either party after\njoinder of issue may demand a trial by jury. The demand must be made in\nwriting and must be filed with the clerk with the notice of trial set\nforth in § 1301. Any other party to the action within ten days after the\nservice of a copy of the notice of trial upon him unaccompanied by a\nwritten notice demanding a trial by jury, may serve upon the attorneys\nfor all the other parties to the action a written notice demanding a\njury trial and file a copy of such notice with the clerk within three\ndays after service thereof. In a summary proceeding to recover\npossession of real property, the demand may be made by the tenant at the\ntime of answering or by the landlord at any time before the day of\ntrial.\n (b) Unless a demand is made and the jury fee paid as provided in\nsection nineteen hundred eleven of this act, a jury trial is waived.\n (c) The Court may relieve a party from the effect of failing to comply\nwith this section if no undue prejudice to the rights of another party\nwould result.\n