N.Y. Uniform District Court Act Law § 406

§ 406. Summons; service by publication authorized.\n The court, upon motion without notice, shall order service of a\nsummons by publication in an action described in § 405 if service cannot\nbe made by another method with due diligence. Practice and procedure on\nservice by publication shall be governed by the CPLR, except insofar as\nthis act otherwise provides.\n