Pursuit of a wrongful termination lawsuit in an at will employment state can be both extremely time-consuming and expensive and there's no guarantee you'll prevail in the end. Unless this action was in complete contradiction with company/management policy (and you can prove that with published policy,) or you can prove your dismissal violated federal discriminatory statutes based on your gender, age, religious convictions, etc., in all likelihood there's not a great deal you can do, in my opinion. Technically, the employer isn't required to state a particular reason when terminating an employee and you could potentially face years in litigation (not to mention thousands of dollars in legal fees) before that final determination is made. That being said, I'm not discouraging any action; simply stating upfront this is an extremely difficult case to prove (and prevail.) Best bet is to contact an employment attorney for a more concise evaluation of your particular circumstances. You may also want to contact your local department of labor as well.

I'm more curious about the outcome of the arrest. An arrest doesn't necessarily lead to conviction in most jurisdictions. Were the charges dropped? Were you convicted? Depending on those circumstances (and that outcome,) you may have different recourse. If it can be proven that the charges were dropped & then determined to be completely untrue (false,) I think you may have other legal options available. Again, that can better be determined by an attorney, but personally, I think worth investigating. *You didn't indicate either way, but this is obviously assuming you've done nothing wrong.

Good luck.