(1) As against its customer, a bank may charge against his account any item which is otherwise properly payable from that account even though the charge creates an overdraft. (2) A bank which in good faith makes payment to a holder may charge the indicated account of its customer according to (a) the original tenor of his altered item; or (b) the tenor of his completed item, even though the bank knows the item has been completed unless the bank has notice that the completion was improper.
New York Legal Code