WA state probate laws and procedures, legal obligations to beginning probate and paying bills, survivorship bank accounts

First, if this was a true "survivorship" type of an account, you might not have had a legal obligation to pay the bills. You might be able to file a claim for reimbursement in the probate. Talk to a knowledgeable probate lawyer in the state where the probate is taking place.

Second, depending upon the size of your mother's estate, the executor could need to know how much was in the accounts for either estate tax or inheritance tax purposes - even though the accounts passed to you, legally they were part of your mother's estate for estate tax purposes. I don't know if the state in which she lived had separate inheritance taxes, but it's possible that there were inheritance taxes, too. It would be the executor's responsibility to pay for these out of the estate and, possibly, to seek reimbursement from you.

This information is not intended to substitute for professional legal advice and does not create an attorney-client relationship. You should accept legal advice only from a licensed legal professional with whom you have an attorney-client relationship.