New York Consolidated Laws, Civil Practice Law and Rules - CVP § 1007. When third-party practice allowed

(a) After the service of a defendant's answer, the defendant may proceed against a person or legal entity not a party who is or may be liable to that defendant for all or part of the plaintiff's claim against that defendant, by filing pursuant to section three hundred four of this chapter a third-party summons and complaint with the clerk of the court in the county in which the main action is pending, for which a separate index number shall not be issued but a separate index number fee shall be collected.  The third-party summons and complaint and all prior pleadings served in the action shall be served upon such person or legal entity within twenty days of the filing.  A defendant serving a third-party complaint shall be styled a third-party plaintiff and the person or legal entity so served shall be styled a third-party defendant.  The defendant shall also serve a copy of such third-party complaint upon the plaintiff's attorney simultaneously upon issuance for service of the third-party complaint on the third-party defendant.

(b) A defendant shall not file a third-party summons and complaint more than ninety days after serving its answer without an order of the court.

(c) No third-party summons and complaint may be filed after the filing of a note of issue unless upon good cause shown or in the interest of justice.

(d) An action filed in violation of this subdivision shall be severed or dismissed without prejudice.

(e) Notwithstanding subdivisions (b) and (c) of this section, a defendant or third-party defendant may file a third-party summons and complaint against an employer of the plaintiff without an order of the court within ninety days after the later of:  1. the date the identity of the employer of the plaintiff becomes known to the defendant or third-party defendant, or 2. the date the defendant or third-party defendant knows or should know the plaintiff sustained a grave injury, as such term is defined in section eleven of the workers' compensation law.

(f) In the event a third-party action is severed from the initial action pursuant to this section, and a third-party plaintiff proceeds to initiate a new action by the filing of a summons and complaint against a severed third-party defendant, any motion to consolidate such actions shall not be permitted.