N.Y. Partnership Law § 115-B
In any action specified in section one hundred fifteen-a of this article, unless the contributions of or allocable to plaintiff or plaintiffs to partnership property amount to five percent or more of the contributions of all limited partners, in their status as limited partners, or such contributions of or allocable to such plaintiff or plaintiffs have a fair value in excess of fifty thousand dollars, the limited partnership in whose right such action is brought shall be entitled at any stage of the proceedings before final judgment to require the plaintiff or plaintiffs to give security for the reasonable expenses, including attorneys' fees, which may be incurred by it in connection with such action and by the other parties defendant in connection therewith for which the limited partnership may become liable under this article under any contract or otherwise under law, to which the limited partnership shall have recourse in such amount as the court having jurisdiction of such action shall determine upon the termination of such action. The amount of such security may thereafter from time to time be increased or decreased in the discretion of the court having jurisdiction of such action upon showing that the security provided has or may become inadequate or excessive.
N.Y. Partnership Law § 115-B