When my uncle passed away, I was his sole heir and had to find his various accounts (sadly, not enough to make me rich beyond my wildest dreams or start my own publishing company

).
If it is the character's own account, then it's the usual ID and such. You fill out a check or a withdrawl slip, prove that you are who you are, toss aside the "don't you want this as a cashier's check" questions, and trot off with the cash.
However, if it is someone else's account, then not only do you have to prove who you are, but you have to prove that you have a right to that money (death certificates and copies of wills, for starters).
Safety deposit boxes are only held for accounts that are active. Meaning, if all there is active at the bank is the safety deposit box, it would have been required to be turned in (to the box owner or to the state) after a set amount of time. I believe it's longer in CA than it is in MA, but all the states have laws about how long any bank account, etc., can lie dormant with no actual ownership. If there are no heirs found in time, the contents revert to the state (which is why they have all those laws, to get the money).
From a fiction standpoint, if you're trying to have him face a challenge getting it, the suggestion that he's acting weird or crazy could work well. At my bank, if I came in acting bizarrely, and therefore differently than every other time they've seen me, the tellers would indeed be checking on me, and the chances of them calling the bank manager or my banking consultant would be high. The banks try to protect you from yourself BUT there is only so much they can do. If you go nutso and they can't talk you out of it, and you can prove it's yours, you can take out that $9K and hand 20's to everyone who passes you by and the bank cannot stop you.