My father passed & did not leave a trust nor will. He had no property & I'm trying to get his checking account closed.
Family Law Attorney
If the estate is small (less than $150,000 in total gross value) and if is really small, then suggest that you just file an affidavit under 13100 and do it your self. Seek help at the local courthouse at their self-help office on doing this. If the estate is just the issue of a small bank account, don't suggest getting a lawyer but use the Small affidavit under Probate Code Section 13100 to get this done.
Estate Planning Attorney
I agree with Attorney Benton. If the only asset was a bank account worth less than $150,000, you should be able to close it 40 days after the date of death by filling out a "Small Estate Affidavit" at the bank. You would need to share the money that's left over with other heirs; and you would be responsible for paying your father's bills.
If the bank account is worth more than $150,000 you will need to file a probate and go through the full process. It is possible but difficult to do this on your own without an attorney.
I am sorry for your loss. If he only had a checking account and the amount in the account is less than $150,000, you can do a small estate affidavit and have the account distributed to his legal heirs. If he owned more assets that exceed $150,000, you should hire an attorney to petition the court for probate and get Letters.