N.Y. Civil Practice Law & Rules § 409
Rule 409. Hearing. (a) Furnishing of papers; filing. Upon the hearing, each party shall furnish to the court all papers served by him. The petitioner shall furnish all other papers not already in the possession of the court necessary to the consideration of the questions involved. Where such papers are in the possession of an adverse party, they shall be produced by such party at the hearing on notice served with the petition. The court may require the submission of additional proof. All papers furnished to the court shall be filed unless the court orders otherwise.