It is a crime to knowingly write a bad check. You could turn over the check to the district attorney but it is up to the district attorney whether or not to press charges. You could also sue her in small claims court.
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Can someone? Yes. Will they? It's unlikely. But you can file a police report and sue her in small claims court.
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Under the facts you listed this sounds more like a civil issue than a criminal one.
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You are probably more interested in getting your money returned. This would be best achieved through small claims court.