If you were the beneficiary of the account, the bank would almost certainly tell you. I believe what they are telling you is that you are NOT the beneficiary of the account at that bank. It is likely it would be part of the estate. I would send a written request for information to the personal representative.
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If the bank is asking for letters of administration-a POD beneficiary does not exist.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.
Pay on Death designations will merely require the identification of of the Payee. A Letter Testamentary pertains to a Probate Case. Sit down with an Estate Planning attorney. Take your documents with you for the consultation. See Avvo.com under Find-A-Lawyer. Good Luck!