Actually, Tennessee vs. Garner weighs heavily against the officer in this case. Unless he can show there was probable cause to believe that the suspect was going to cause death or serious injury to the officer (impossible, as the suspect was unarmed and running away) or others (pretty much impossible as well I suspect), then Tennessee vs. Garner says the officer had no authority to shoot.
[charlesjohnson 4/10/15]
....The key part comes next, and was also cited in the recent DOJ report on the Mike Brown shooting:
It is not, however, unconstitutional on its face. Where the officer has probable cause to believe that the suspect poses a threat of serious physical harm, either to the officer or to others, it is not constitutionally unreasonable to prevent escape by using deadly force. Thus, if the suspect threatens the officer with a weapon or there is probable cause to believe that he has committed a crime involving the infliction or threatened infliction of serious physical harm, deadly force may be used if necessary to prevent escape, and if, where feasible, some warning has been given. As applied in such circumstances, the Tennessee statute would pass constitutional muster.
Read more at http://bit.ly/1Gxj7bU