No there was a crime committed here by Zimmerman. Zimmerman according to Fla law can't claim self defense.
This part of Fla self defense law
http://licgweb.doacs.state.fl.us/weapons/self_defense.html
First off, Trayvon Martin was not commiting a crime. That is a fact. When Zimmerman approached Trayvon Martin the first time, the youth fled. Zimmerman was not in any danger. But Zimmerman than looked for a found the young man again. At that point, Zimmerman is the agressor and Trayvon Martin according to Fla law could use any force necessary to ward off an asssailant, including deadly force.
He fought off Zimmerman which was in his right, his right to not retreat. In response Zimmerman shot and killed the youth. Zimmerman initiated the confrontaiton and he was the agressor. Martin, the victim was well within his rights to fight off an unknown assailant who had chased him and found him a
second time. Also according to Fla law, using a gun to kill a person in a fist fight is not lawful.
Trayvon Martin committed no crime and possessed nothing illegal. Zimmerman possessed no legal authority to question or pursue Martin.