Not with "stand your ground" law.
Stand you Ground does NOT mean that the police CANNOT arrest someone, it means that in Court you can ask a Judge to dismiss the case because you were acting in self defense
Once again SYG is a Legal defense intended for Court of LAW, it is NOT for the police to decide that they can't arrest you once you have said that....
They can and do arrest people who shoot other people, no matter what they say during questioning, they can investigate, and they turn the evidence over to the Prosecutor who decides who to charge and with what,
The Police should not unilaterally decide that this is a self defense case and just not do their job Because that decision rightfully belongs in Court.