Under U.S. law the fleeing felon rule was limited in 1985 to non-lethal force in most cases by Tennessee v. Garner,471U.S.1. The justices held that deadly force "may not be used unless necessary to prevent the escape and the officer has probable cause to believe that the suspect poses a significant threat of death or serious bodily harm to the officer or others."[2]
A police officer may not seize an unarmed, nondangerous suspect by shooting him dead...however...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.
Fleeing felons may be followed into places not open to the public without a warrant if the officer is in "hot pursuit."[4]
Case law
Samuel Alito's memo written while working in the Solicitor General's office regarding Memphis Police v. Garner, which was the Sixth Circuit appellate case leading to Tennessee v. Garner.[5] (May 18, 1984) (PDF)