N.Y. Crim. Proc. Law § 520.40
When a local criminal court acquires control over the person of an accused and such court designates the amount of bail that the accused may post and such bail is posted in cash and subsequently the accused is arraigned in superior court where bail is fixed by such court, the accused may request that the cash bail posted in the local criminal court be transferred to the superior court. Notice of such request must be given to the person who posted cash bail. Upon such a request the superior court shall make an order directing the local criminal court to transfer the cash bail that it holds to the superior court for use in the superior court. If there is an overage, the superior court shall order it be paid over to the person who posted the cash bail in the local criminal court. If there is a deficiency, the accused shall post additional bail as directed by the superior court.
N.Y. Crim. Proc. Law § 520.40