Second, you haven't made it clear whether the hitter is under criminal investigation, so you can't be sure whether he is in criminal proceedings for the time being.
Third, the doctor's certificate will turn intentional injury into intentional injury and serious injury, and if it is intentional in criminal proceedings, it will constitute perjury; If not, the injured party only wants to solve it privately, which may constitute a crime of abuse of power.
To sum up, since the public security has entered the investigation procedure, how to solve it depends on the law.