You should only attempt this through your attorneys efforts. Until there is no possibility of the charges against you being filed I would recommend you make no statements and let your attorney guide you through the process imcludind sealing or expunging the record of your arrest if eligible.
If the charges get dropped, you are not necessarily "found innocent". Hopefully a lawyer and/or public defender are helping you with this. If the charges do get dropped, you can sue the other person for defamation, malicious prosecution among other things. For the most part, most lawyers will not take a case like that on a contingent fee but rather an hourly retainer which could be very expensive. Most civil lawyers will not start a case less than 2500 to 5000 dollars down and that is only a retainer. You also should seek an attorney out to help you expunge your record if you are eligible and do not have any other convictions on your record. Good luck to you!
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DA does the charging decisions, and you can start with him on the criminal side, aided perhaps by your state assembly/house rep, state senator, and congressman if the eggregiousness of the facts cry for redress.
Definitely hire an attorney for any expungement as a wrong move can't necessarily be "done over". You will need factual findings, and maybe a reasoning by the DA as to why he didn't file (and while you or your attorney are at it, ask the DA why he did or did not file a false police report charge against the perpetrator).
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