It is legal for police to hit you but only under specific circumstances and within the bounds of what is considered to be reasonable force.
The key to the reasonable force that justifies the police hitting you is that the force used must be proportional to the threat or resistance.
Police can generally use force to make an arrest or prevent escape or overcome any resistance, although the police cannot engage in acts of brutality or use excessive force.
For example if someone is punching them and they cannot get to their taser or pepper spray in time or gun and they fear for their life and need to stop the beating of them, then they could punch the suspect back or hit them to get them under control and prevent further injury themselves.
Just like civilians can legally hit someone or punch them back or beat up on someone in self defense, the police can also do the same even when on duty.
Although the police cannot simply beat up on someone or punch them or kick the person just to do so.
They have to be actually defending themselves.
If a suspect is fleeing, a verbal warning may be sufficient although if the suspect resists the police, then the police may need to use more force, but still within reasonable bounds.
Use of deadly force like shooting a suspect is only permitted when the police has reasonable belief that the suspect poses an imminent threat of death or serious bodily harm to the police of others.
The police cannot just shoot a suspect just because they are running away or not complying.
Using excessive force, or any force beyond what is considered to be reasonable, is illegal and can result in the police receiving disciplinary action, lawsuits or even criminal charges.
Although, while officers or police cannot generally raise self defense as a justification for using force against a civilian, the police can use force to defend themselves if they are under attack or they reasonably believe they are in imminent danger.
Police go through extensive training on the use of force, including de escalation techniques and the use of various tools and weapons.
Police officers are subject to accountability for their actions and use of excessive force can lead to disciplinary action, lawsuits or criminal charges if they could've use less excessive options to get the suspect to comply.