Adding to Feetwet's answer, in Souza v. City of Antioch it was ruled that "Police officers have no affirmative statutory duty to do anything", and in calling on common law concepts of duty, one must distinguish misfeasance and nonfeasance (doing badly and not doing). Drawing from the decision, "one person owed no duty to control the conduct of another":
the police owe no duty to crime victims in those cases where they have
not acted to protect them, i.e., cases of nonfeasance. In contrast,
when the police actively involve themselves in situations where a
third party threatens another, we have imposed upon them an
affirmative duty, generally under the rubric of a “special
relationship” with either the victim or the actor, to exercise
It is more the rule to let political disturbances burn themselves out quietly, rather than aggressively arrest everyone who might be charged with a crime, because (1) such intervention can exacerbate the situation and (2) it can create a "special relationship" where the police do become liable.