Answer:
If by "liability to the bank" you mean will the bank incur liability for informing the caller of the account closure or stop payment, the answer is no, as long as those are accurate statements at the time. The Gramm-Leach-Bliley Act privacy regulations hold an exception for the sharing of such information under such circumstances. I would not recommend providing any background on the account closure (customer request/bank request, for example) or for any reason the customer may have offered for stopping payment.
First published on BankersOnline.com 8/23/10