N.Y. UJC Law § 1303

§ 1303. Jury trials; how obtained; jury fee.\n (a) If the defendant appears before the clerk to answer in person, he\nshall demand a jury trial, if desired, at that time. If he does not do\nso, any other party may demand trial by jury by mailing such a demand to\nthe clerk and all other parties within three days after receiving notice\nof the trial date as set forth in § 1301(a).\n (b) If a motion is made to have a trial date set, as provided in §\n1301(b), the movant shall include demand for trial by jury, if desired,\nin his notice of motion. If he omits to do so, any other party desiring\ntrial by jury shall demand it in papers opposing the motion.\n (c) If the trial date is set by agreement pursuant to § 1301(c), the\ntrial shall be without jury unless the stipulation provides otherwise.\n (d) The party demanding trial by jury shall pay the fee therefor upon\nmaking the demand. If trial by jury is stipulated to, the stipulation\nshall provide for payment of the jury fee, and in the absence of\nproviding therefor, it shall be paid by the plaintiff.\n (e) Unless a jury is demanded or stipulated to, and the jury fee paid\nas provided in section nineteen hundred eleven of this act, trial by\njury is waived.\n (f) 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