If it's a joint bank account with your name on it, yes. If the credit card debt is only in the deceased person's name, but the bank account is in both of your names, you don't need to pay the debt from that account unless a probate judge directs you to do so. If your name is not on the bank account, you will need to follow procedures as set up in the deceased person's will. Taking money from a deceased person's bank account without your name on it could be a criminal offense in your state. Check with a probate lawyer on how to proceed.