Depends entirely on what they are asking for.
There is an exception for some types of requests from the Department of Veterans Affairs. It is found in Section 3413(p) and reads as follows:
(p) Access to information necessary for administration of certain veteran benefits laws
(1) Nothing in this chapter shall apply to the disclosure by the financial institution of the name and address of any customer to the Department of Veterans Affairs where the disclosure of such information is necessary to, and such information is used solely for the purposes of, the proper administration of benefits programs under laws administered by the Secretary.
(2) Notwithstanding any other provision of law, any request authorized by paragraph (1) (and the information contained therein) may be used by the financial institution or its agents solely for the purpose of providing the customer's name and address to the Department of Veterans Affairs and shall be barred from redisclosure by the financial institution or its agents.
Note that it is a very narrow exception and only allows you to provide name and address.