Are you dealing with a big bureaucracy police dept or a small town dept?

Do you have a record of whom you talked to when you contacted the dept. about the status of you car?

If you are unhappy with the first answer you rec'd are you willing to escalate your complaint up the chain of command.  A Sergeant may not be able to satisfy you and a Captain may have the clout to do so.

On the facts you presented you may be responsible for the tow but not any storage charges.