It's highly unlikely that you have a law suit against the city or county for many reasons.
First, it's difficult to establish negligence in the performance of investigative duties. Second, most jurisdictions exempt discretionary functions to civil liability. Third, this is a discretionary decision to arrest someone else; discretionary governmental decisions are rarely subject to civil liability. Fourth, you are not the party directly affected; you are only indirectly affected by the possible evdientiary value of a conviction. Fifth, it would be exrtremely difficult to prove that (1) the person would have been convicted, and (2) that conviction would have resulted in a higher civil recovery for you.
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