N.Y. Real Property Actions & Proceedings Law § 735
1. Service of the notice of petition and petition shall be made by personally delivering them to the respondent; or by delivering to and leaving personally with a person of suitable age and discretion who resides or is employed at the property sought to be recovered, a copy of the notice of petition and petition, if upon reasonable application admittance can be obtained and such person found who will receive it; or if admittance cannot be obtained and such person found, by affixing a copy of the notice and petition upon a conspicuous part of the property sought to be recovered or placing a copy under the entrance door of such premises; and in addition, within one day after such delivering to such suitable person or such affixing or placement, by mailing to the respondent both by registered or certified mail and by regular first class mail,
2. The notice of petition, or order to show cause, and petition together with proof of service thereof shall be filed with the court or clerk thereof within three days after;