N.Y. UJC Law § 1806

§ 1806. Trial by jury; how obtained; discretionary costs.\n A person commencing an action upon a small claim under this article\nshall be deemed to have waived a trial by jury, but if said action shall\nbe removed to a regular part of the court, the plaintiff shall have the\nsame right to demand a trial by jury as if such action had originally\nbeen begun in such part. Any party to such action, other than the\nplaintiff, prior to the day upon which he is notified to appear or\nanswer, may file with the court a demand for a trial by jury and his\naffidavit that there are issues of fact in the action requiring such a\ntrial, specifying the same and stating that such trial is desired and\nintended in good faith. Such demand and affidavit shall be accompanied\nwith the jury fee required by law and an undertaking in the sum of fifty\ndollars in such form as may be approved by the rules, payable to the\nother parts or parties, conditioned upon the payment of any costs which\nmay be entered against him in the said action or any appeal within\nthirty days after the entry thereof; or, in lieu of said undertaking,\nthe sum of fifty dollars may be deposited with the clerk of the court\nand thereupon the clerk shall forthwith transmit such original papers or\nduly attested copies thereof as may be provided by the rules to the part\nof the court to which the action shall have been transferred and\nassigned and such part may require pleadings in such action as though it\nhad been begun by the service of a summons. Such action may be\nconsidered a preferred cause of action. In any small claim which may\nhave been transferred to another part of the court, the court may award\ncosts up to twenty-five dollars to the plaintiff if he prevails.\n