Man I hope this blows over for you and you don't get in further trouble.
Ultimately, this is true:
There is literally no way for you to be charged with the crime without evidence. A single accusation can't affect your criminal record; it can only get you fired.
They must have evidence "beyond a reasonable doubt" or the charge will be dropped.
tldr; it's a scare tactic. don't admit to anything.
But if I were you I would try to be cooperative and friendly. Getting fired is bad, and already being in hot water, being aggressive about your point of view (as I've seen several forumers in past threads recommending) will get you fired and make it harder to find another job. A theft accusation on top of overassertiveness (not sure if a word, but you get it) will look really bad if they contact previous employers. I can guarantee that'll be catastrophic for a law enforcement career.
Best wishes to you.