My personal suggestions:
1. You need to evaluate the situation. If this is the one-time thing, maybe just forget it. If it is very likely that same thing will happen again, you should pursue the legal approach.
2. You should call police about what happened to your child. The police will make investigation and report to prosecutors who will determine if charges will be issued.
Even if the police or prosecutor decides not to go further, the person who really hit your child will learn a lesson too because the police definitely will talk to him.
3. In U.S., many people have been convicted without solid evidence or witnesses. It seems that Chinese people tend to think witness and evidence are essential factors to make one convicted. It is not true in U.S.. Eventually if this case appears in court, many details will be revealed just by words. As long as the jury believes it has really happened, then he will be convicted.