According to the "Stand you Ground Law" can shoot an unarmed individual if they are trying to harm you. All the man has to say is that the kid attacked him.
We also believe murderers when they say they didn't do it either.
While I can understand the stand your ground laws, I don't see how they apply to someone who was actively pursuing the victim especially after the person was instructed by authorities not to leave their property. It is pretty obvious that even if the child did actually attack Zimmerman, that attack was provoked by Zimmerman.
The state has a responsibility to arrest Zimmerman because someone is dead, killed by the weapon Zimmerman owns. That is a crime in itself. Secondly Zimmerman has admitted to shooting the child and thus has to stand trial for at least manslaughter. It is here where the judge or jury can decide if he did so in self defense. That is not a call for the police to make.
Lastly, given what is known about this case, the previous conviction of Zimmerman, as well as the conversation on the 911 recording, a pretty solid case can be made for not only murder but also a hate crime. At the very least a straight up manslaughter charge because none of this would have happened if Zimmerman did not pursue the boy and provoke an altercation. The age, weight difference, contents of pockets and witness reports all prove that the boy would just have continued on walking home back from the shops if Zimmerman had done as he was told by the 911 dispatch.
Further, all of what I have stated is still the best case scenario where the boy actually attacked Zimmerman for following him, and not the more likely event that Zimmerman accosted the boy which caused a struggle probably, and resulted in Zimmerman killing the child.
Oh and police are expected to arrest everyone who commits a crime, they then have the option of bail which can be denied by a judge if the person is considered a flight risk. Regardless though they first have to be arrested.