N.Y. Jud. Law § 758
Where it is prescribed by law, or by the rules of civil practice, that a notice may be served in behalf of a party, upon a sheriff or other person, requiring him to return a mandate, delivered to him, or to show cause, at a term of a court, why he should not be punished, or why an attachment should not be issued against him, for a contempt of the court; the party, in whose behalf the notice is served, may, at the time specified therein, file with the clerk, proof, by affidavit or other written evidence, of the delivery of the mandate to the accused; of the default or other act, upon the occurrence of which, he was entitled to serve the notice; of the service of the notice; and of the failure to comply therewith. Thereupon the proceedings are the same, as where an order to show cause is made, and it, and a copy of the affidavits upon which it is granted, are served upon the accused.
N.Y. Jud. Law § 758