If the facts are exactly as you state them in this question, the police officer has probably committed a crime. This is because the Supreme Court has held, in Tennessee v. Garner, that it is not lawful for a police officer to use deadly force against an unarmed suspect who is running away and does not likely pose a danger to anyone.
In the situation you describe, we can assume that the person who is running away from the scene of the crime does not appear to be dangerous. True, they have apparently committed a felony, but they have no weapon. They are running away from the police, not towards them. They do not appear to be likely to grab a passerby and cause them harm. This means that there is no reason for the police officer to need to use deadly force. In Garner, the Court held that the use of deadly force could only be justifiable if there was probable cause to believe that the suspect was going to either kill or inflict serious bodily harm on the officer or another individual.
For these reason, the police officer in the situation you describe has probably committed a crime.