I am confused about that too. I thought policing was a State responsibility. From what I hear Clinton say, she seems to think it should be taken over by the Feds.
I think Trump is more in line on the matter, backing up the States in their methods of training, equipment, etc.
It's Federal, state, and local (counties and cities). Generally, the Federal police agencies (FBI, DEA, BATF) are permitted only to enforce Federal law.
As you thought, the primary authorizing authority for the ordinary cop on the beat is the state, though she is probably organized as a city or county police force. The structure is established by state law. These cops (and the state police) are empowered to enforce Federal and state laws, and city/county ordinances.
As a practical matter, the cop on the beat ultimately answers to the the chief of police of her force, who answers to the mayor or county executive, in terms of her employment and discipline. If her actions are deemed criminal, she will be tried by the state or the Federal government, depending on whether the crime is state or Federal.
As another practical matter, almost all Federal law violations are also state crimes, so a local cop can arrest you, and let the state's attorney's office and the Fed sort out the prosecutions later.
One of the advantages of a national police force like the Irish Gardai, or a quasi-national force like the RCMP, is that it generally has a better "boots to suits" ratio than our ridiculous mishmash of agencies.
Yes, all lives do matter. There are too many people getting killed, not just black people. The difference is, when a non-black is killed there is no rioting over it. If he was doing something dangerous, his fellow citizens understand that he probably deserved it.
When a black man is killed, the black community, in typical tribal fashion, immediately defend him and place the blame on the police They won't turn each other in like civilized people should or admit that he might have been afoul of the law.
It's not right for police to shoot an unarmed man, that's for sure, but when a suspect is behaving in a dangerous way and gets shot there is no use trying to defend him even though he might be your 'brother'.
From my point of view, the problem is the police are taught to shoot if they see a gun. Soldiers are taught to take cover first. This allows them a few more seconds to assess the situation, and allows them to fire more accurately, if fire they must.
