N.Y. C.P.L.R. 1008

§ 1008. Answer of third-party defendant; defenses. The third-party\ndefendant shall answer the claim asserted against him or her by serving\ncopies of his or her answer upon the third-party plaintiff. The\nthird-party defendant may assert against the plaintiff in his or her\nanswer any defenses which the third-party plaintiff has to the\nplaintiff's claim except an objection or defense that the summons and\ncomplaint, summons with notice or notice of petition and petition was\nnot properly served, or that jurisdiction was not obtained over the\nthird-party plaintiff. The third-party defendant shall have the rights\nof a party adverse to the other parties in the action, including the\nright to counter-claim, cross-claim and appeal.\n