All Trump could do is make a complaint - he cannot file charges. The police or the prosecutor would have to determine if there was evidence of a crime and then decide whether or not to file charges.
This just shows why Trump is such a bad candidate and would be a horrible president. All he or Lewandowski had to do was say, "Sorry, we didn't realize he grabbed you so hard." Instead, they tried to slime and attack the reporter, and they keep doubling down even after proof that they lied about the incident. Instead of focusing on his campaign, he is wasting time tweeting and making silly statements ("her pen could have been a bomb!") over an incident that should have been resolved the day after it happened.
I know. I was encouraging him to file a complaint.
Had he done this it would have been an admission of guilt. She still would have filed a complaint, charges still would have been filed and he would certainly been convicted based on his own apology. In the legal profession we have a word for people who apologize in situations like this - convict.