"QUESTION: Can the police legally use deadly force to make an arrest?
ANSWER: Sometimes. A police officer may use deadly force to capture a suspect only if a suspect threatens an officer with a weapon or an officer has probable cause to believe that the suspect has committed a violent felony (Tennessee v. U.S. Sup. Ct. 1985).
The police can also use deadly force to protect the life of a third person. But police officers can not routinely use deadly force whenever they seek to arrest a suspect for committing a felony. The police should allow some felony suspects to escape rather than kill them." -From, "The Criminal Law Handbook"