N.Y. Gen. Oblig. Law § 15-701

§ 15-701. Surety not discharged by failure or refusal by creditor to\nsue principal debtor. Unless otherwise agreed between the parties in\nwriting, the failure or refusal by a creditor, after a demand by a\nperson bound as surety, to bring an action against a principal debtor\nupon a contract hereafter made or an obligation hereafter created for\nthe payment of money or the performance of any act shall not discharge\nsuch surety.\n