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I am sorry to hear about this situation. I am afraid that someone in your situation cannot sue the company, because the company and its management had no duty to disclose to you that you were under investigation.
However, you can sue the female if she made a false report.
To sue in a state court, one needs to have a "cause of action." There are numerous causes of action, such as "breach of contract," "negligence," "fraud," "unjust enrichment," etc., as well as causes of action rooted in statutory law. Every state has their own although they are very similar to each other in every state because they all stem from the same common law. A pleading in Court needs at least one cause of action, although it is not unusual to have more than one.
The woman can be sued for defamation. Under New York law, the elements of a defamation claim are: a false statement; published to a third party without privilege or authorization; with fault amounting to at least negligence; that caused special harm or defamation per se. Dillon v. City of New York, 261 A.D.2d 34, 38 (N.Y.A.D. 1 Dept. 1999).
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