It is the gentle approach of the bank to visit the family for the payment of outstanding amount from family of the deceased. If you have informed the bank about death of your brother, then bank shall request you to pay.
It shall be decent and responsible of you if decide to pay.
If you want to pay you may ask the bank to provide you complete account statement with break up of principle amount and interest collected, and pay the balance amount or balance from principle amount.
You must not provide your ID or Pan card number /copy etc.
If you have not received any share from estate of your brother then bank may not succeed in getting any recovery from you legally.