If you physically injure/kill someone you have, among other things, violated their civil rights. You do not have to be a government entity/employee to commit this crime. The FBI investigates civil rights abuse cases. Both circumstances have been the way things are ever since the Civil Rights Act of 1964 was passed.
There are folks from all three sides of the fence who are both sitting in a federal prison and under obligation as part of their sentencing to pay large sums of money in compensation for violating the civil rights of those they injured/killed. Not that there's a tinker's chance they will ever actually pay the first penny.
Hope this basic explanation helps.,