The rules dictate when an officer may move from mild coercion, such as issuing an order or grabbing a suspect’s arm, to stronger or even deadly action. In general, officers are allowed to respond with greater force after a suspect does so, and the type of response — from a gentle push to a tight grip, a baton strike to a stun gun shock to a bullet — rises as the threat grows.

Every step, however, is overshadowed by a single imperative: If an officer believes he or someone else is in imminent danger of grievous injury or death, he is allowed to shoot first, and ask questions later. The same is true, the courts have ruled, in cases where a suspect believed to have killed or gravely injured someone is fleeing and can only be halted with deadly force.

“It’s a very simple analysis, a threat analysis,” said Geoffrey P. Alpert, a University of South Carolina professor and expert on high-risk police activities. “If a police officer has an objectively reasonable fear of an imminent threat to his life or serious bodily harm, he or she is justified in using deadly force. And not just his life, but any life.”