New York Consolidated Laws, Civil Practice Law and Rules - CVP § 8501. Security for costs

(a) As of right.  Except where the plaintiff has been granted permission to proceed as a poor person or is the petitioner in a habeas corpus proceeding, upon motion by the defendant without notice, the court or a judge thereof shall order security for costs to be given by the plaintiffs where none of them is a domestic corporation, a foreign corporation licensed to do business in the state or a resident of the state when the motion is made.

(b) In court's discretion.  Upon motion by the defendant with notice, or upon its own initiative, the court may order the plaintiff to give security for costs in an action by or against an assignee or trustee for the benefit of creditors, a trustee, a receiver or debtor in possession in bankruptcy, an official trustee or committee of a person imprisoned in this state, an executor or administrator, the committee of a person judicially declared to be incompetent, the conservator of a conservatee, a guardian ad litem, or a receiver.