New York Consolidated Laws, Civil Practice Law and Rules - CVP § 3011. Kinds of pleadings

There shall be a complaint and an answer.  An answer may include a counterclaim against a plaintiff and a cross-claim against a defendant.  A defendant's pleading against another claimant is an interpleader complaint, or against any other person not already a party is a third-party complaint.  There shall be a reply to a counterclaim denominated as such, an answer to an interpleader complaint or third-party complaint, and an answer to a cross-claim that contains a demand for an answer.  If no demand is made, the cross-claim shall be deemed denied or avoided.  There shall be no other pleading unless the court orders otherwise.