N.Y. Jud. Law § 778

§ 778. Prosecution of undertaking by person aggrieved. The order\ndirecting the undertaking to be prosecuted, may, in the discretion of\nthe court, direct the prosecution thereof, by and in the name of any\nparty aggrieved by the misconduct of the accused. In such a case, the\nplaintiff may recover damages, to the extent of the loss or injury\nsustained by him, by reason of the misconduct, together with the costs\nand expenses of prosecuting the special proceeding in which the warrant\nwas issued; not exceeding the sum specified in the undertaking.\n