"A day late..." but
Came across this researching something else and felt compelled to reply in the event that others are referring to this thread for current matters.
First, you need to consult your state's version of the Uniform Commercial Code (UCC). Regarding checks ("negotiable instruments"), there are two banks involved: the depositary bank and the drawee bank. Ordinarily, the depositary bank bears the risk of loss (between the two banks) in the event of a fraud, because they are the first to see the check. They are in the best position to scrutinize its legitimacy. In that situation, the depository bank will go to the person who presented the check to be cashed and ask for the funds and/or unilaterally take the funds out of the account that person has with them
Secondly, you need to check your state's laws on conversion as this would be the likely action brought against you. Simply, this is treating someone else's property as your own.
The overlapping factor in both items above appears to be the banks odd willingness to cash this check. Two things come to mind:
(A) They cashed out a $16,000 check (a large amount) for an individual who didn't even have a checking account, let alone any account, with their bank. I was under the impression that most banks won't cash a cashier's check unless you have an account with them AND this account has funds matching the cashier's check. When your available funds are less than the cashier's check they may cash that portion of the check, but the remaining amount is held until the drawee bank (the bank that issued the check) confirms the funds are available.
(B) Here, the drawee and depository bank are the same! Accordingly, one would think it would be very easy for the teller to identify a fake cashier's check that purports to be one issued by its own bank. Secondly, if it was an actual B of A cashier's check but it had been altered, there may be a question as to whether B of A should have recognized this sooner. How long did it take for them to contact you about the problem?
At bottom, it's clearly not your money and the situation will resolve itself if you simply return it. That said, you should look into what was discussed above and consider how long it took the bank to notify you of the problem. Did you spend some of the money in the interim? Look into whether your inability to pay back the full amount, as here, is justifiable. Of course, common sense would dictate that the more you can return to the bank the better. If you spent the entire $16,000, you may be out of luck even if the bank's practices were questionable.
(C) This is a good OFFICIAL resource for addressing common questions. In your situation, the depository and drawee banks are the same so it doesn't strictly fall under any of the questions addressed:
http://www.helpwithmybank.gov/get-answers/bank-accounts/forgery-and-fraud/bank-accounts-forgery-fraud-quesindx.html
(D) The police officer probably gave you some good advice. I doubt he meant that you should keep the money indefinitely. However, if the bank decided to pursue a civil action against you returning the money would support their assertion that you knew it did not belong to you all along. This would put you in a tough spot. If you find yourself in this situation I would recommend you consult an attorney, before returning the money, so that you can work out a legally binding agreement with the bank whereby they agree not to sue you if you return the money. This is especially important if you can't return all of the money. The bank could turn around and sue you for the remaining amount; again, asserting that your return of the money is proof you knew the entire amount wasn't yours from the get go.
DISCLAIMER: I'm not an attorney, but I've had to look into this stuff for personal reasons--your state's UCC is publicly available online most likely. This is intended to point you in the right direction for research purposes and you should not rely on anything I stated. Always verify things for yourself and consult a licensed professional. If you do so, perhaps this will facilitate a more efficient conversation.