The law is a funny thing. Many people think that those knowledgeable in the law give answers, while most who have some knowledge ask questions and make arguments.
Criminal law tends to have two parts, the act and the mental state. The mental state is often the hardest to prove. Thanks to your question, if we find some act which would be a crime when combined with your deliberate, intentional state of mind, we have a completed crime.
Of course, not telling the bank you have some money of theirs is probably not a crime as there is no act. I'm not sure you have a duty to tell the bank under AZ statutes. But, now *my* question.
How are you going to get it out?
The act of writing a check or a withdrawal slip changes things. You know the money is not yours. You've said as much. That's too bad for you as that is the hard part to prove--what you know. Now, when you do the act to get the money, the bank may argue it was in your care and then it would be embezzlement. Or, it could be a simple fraud. In Arizona, any person who, pursuant to a scheme or artifice to defraud, knowingly obtains any benefit by means of false or fraudulent pretenses, representations, promises or material omissions is guilty of a class 2 felony. We could look farther, but will find some larceny involved.
I sense a whiff of homework and hope I did nothing more than point you in a direction. If I'm wrong, I'm pleased your questions have made it impossible to claim "oops" (meaning lack of intent) when you are caught by anyone with anything more than a cursory investigation.
Info edit:
If you did take the money, it would be income in the year in which you had constructive receipt. If you are audited before the crime is committed (when you have not done an act), you may have some explaining to do if the amount is large. One method the IRS uses in audits is called a "T" account. They put all the income on one side and all the expenses on the other. You will need to have reported all your income. While the IRS does not often put people in jail for claiming too many deductions against income, people who don't report income are at some risk. "You see your honor, I wasn't committing tax fraud. I was waiting for the bank to forget about the mistake so I could steal the money without anyone knowing."
Heck of a defense. Weird thing is, it might actually work as intent is the hard thing to prove in those types of cases as well. I mean, except for the question which just gave you the knowledge. Intent city!