N.Y. New York City Civil Court Law § 1608
Whenever judgment shall be rendered on the bond of a marshal, or the bond shall be reduced as provided in the last preceding section, the city clerk shall report the fact to the appellate division. If the amount of the judgment is equal to or greater than the amount of the bond the appellate division shall direct the marshal to furnish a new bond; or, if the amount of the judgment is less than the amount of the bond, or in case of a reduction thereof, the appellate division shall direct the marshal to furnish an additional bond in the penal sum of double the amount of the judgment or the reduction. If the marshal fails to comply with such direction within ten days after notice thereof, his failure shall constitute ground for his removal from office.
N.Y. New York City Civil Court Law § 1608