That's a much larger question than can be answered from a few paragraphs. Police are responsible for whatever they do, but there are also many defenses they can raise.
You need a lawyer.
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Based solely on the limited information you have provided in your post, your son could have a potential Section 1983 claim. (Shooting a fleeing felon in the back is very rarely justifiable.) Your son needs to contact a local civil rights attorney. Just, please, be aware that in claims against public entities, the statute of limitations is shortened and requires an administrative claim be filed first (so, don't waste time).
Ms. Berjis is licensed to practice law in the State of California. The laws of your jurisdiction may differ and thus this answer is for informational and educational purposes only and is not to be considered as legal advice. Since all facts are not addressed in the question, this answer could change depending on other significant and important facts. This answer in no way constitutes an attorney-client relationship.
Police misconduct matters - deadly force cases in particular - are among the toughest cases around. In general terms, the facts you have offered here may possibly give rise to a claim under either Georgia law, federal constitutional law, or both.
Under your version of the facts, the underlying stop - person of interest - would be most analogous to a Terry stop, meaning that the police had reasonable articulable suspicion to briefly detain your son. If your son responded by offering violence to the officers, that would give them probable cause to arrest him for obstruction. If he had a weapon, particularly a gun, the officers are allowed to respond with force that is at least one step higher on the force continiuum from the threat they are facing. So, if your son had a gun, they would be authorized to use deadly force to respond to the threat.
Once he runs away (and depending on whether he was still armed or the officers had reason to believe he was armed), justifying the use of deadly force to stop him may be harder for the officers. Officers are only authorized to use deadly force to prevent the escape of a dangerous fleeing felon or someone who continues to present an imminent threat of bodily harm to the officers or others.
I would strongly encourage you to contact an attorney who specializes in police misconduct matters and has previously handled a police shooting case. There are several good lawyers in Atlanta who practice in this area. They include Cary Wiggins, Albert Wan, Craig Jones and Bryan Spears. Our law firm also handles these matters. You can learn more about us on our website or my page on AVVO.com
This response is provided for informational purposes only. It is not a consultation and is not legal advice. You should not act or fail to act in reliance upon the information provided in this response. This communication does not establish an attorney-client relationship between you and our Firm. You should always consult with an attorney prior to taking any action with regard to a potential legal problem.