Police officers are generally allowed to use reasonable force to take a person into custody. For example, if a suspect resists by momentarily attempting to run away or giving a token push, an officer wouldn't be justified in using extreme force. If officers use unnecessary force, they can be subject to serious repercussions, including criminal prosecution and civil liability (in the form of lawsuits by victims).
Courts decide whether an officer's use of force was unreasonable on a case-by-case basis, taking into account:
The amount of force that police officers can use when making an arrest is a subject of much concern and controversy. Police officers have discretion to use as much force as they—at the time of arrest—reasonably think necessary to protect both the public and themselves. But citizens' groups, especially those made up of ethnic or racial minorities, often oppose the way police officers employ force. They claim that police regularly overstep the bounds of necessity. Consider the following example.
Too much. Officer Smith and his partner observe Delany punch someone outside a bar and then run away. The officers give chase. When they catch up, Delany struggles and strikes at the officers in an effort to escape. While Officer Smitts applies a chokehold, the partner manages to handcuff Delany and manacle his legs. However, Officer Smitts continues to apply the chokehold for another minute, until Delany passes out. Officer Smitts used excessive force and may be subject to a range of outcomes, including discipline from the police department. (His conduct, however, doesn't affect Delany's criminal liability for the punch.)
The U.S. Supreme Court established that that a police officer who has probable cause to believe a suspect poses a threat of serious harm to the officer or others may use deadly force to prevent escape. (Tennessee v. Garner, 471 U.S. 1 (1985).) This might happen, for instance, if the suspect threatens the officer with a gun. The Court, however, indicated that officers should issue warnings when possible. It also held that deadly force is unjustified when the suspect poses no immediate threat to the officer and no threat to others.
For more on related topics, see Arrests and Probable Cause.