There are no national studies of police brutality. From time to time a local group does a study to prove a pattern of excessive force or racism. Sometimes a department does a study to defend itself. The statistical study promised by the Justice Department, of complaints it has received about local police, should be a useful collection of data and guide to further research. Shooting by police has been much studied.
Some lessons apply to other excessive force.
Police shoot at blacks proportionately more than at whites. Blacks commit violent crimes proportionately more than whites. Most likely, police are not racist in their decisions to shoot. More important, rules and training to reduce shooting by police do work. They also result in fewer police injuries and deaths.