Supreme Court said it is a 4th amendment violation to kill a fleeing suspect just for fleeing. They can only use deadly force if the suspect is reasonably believed to be a significant threat to life or injury to the officer or another person.

The state police officer shot and killed Garner as he was fleeing the scene of the crime. Despite knowing that Garner was unarmed, the police officer believed that he was justified in shooting him to prevent his escape. Garner's father brought a constitutional challenge to the Tennessee statute that authorized the use of deadly force in this situation. The state prevailed in the trial court, but the state appellate court ruled that the statute was unconstitutional.

https://supreme.justia.com/cases/federal/us/471/1/#:~:text=Under%20the%20Fourth%20Amendment%20of,to%20the%20officer%20or%20others