Legal in Tennessee unless posted, and I've never seen one posted. I ignore "No Weapons" signs. I don't carry weapons, only tools.
Only state that forbade carry in banks I ever heard of was North Carolina. Can anyboy from NC confirm?
Montana also does not allow bank carry: Montana Code 45-8-328 (b) a bank, credit union, savings and loan institution, or similar institution during the institution's normal business hours. It is not an offense under this section to carry a concealed weapon while: (i) using an institution's driveup window, automatic teller machine, or unstaffed night depository; or (ii) at or near a branch office of an institution in a mall, grocery store, or other place unless the person is inside the enclosure used for the institution's financial services or is using the institution's financial services. From the Montana Statutes.