That is the prerogative of the police because they are the executive branch of the government. The accused is presumed innocent until proven guilty and needs an attorney.
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In Pennsylvania, a criminal caption will read Commonwealth of Pennsylvania v. John Doe. It is the Commonwealth, and not the victim of the alleged crime, that brings the charges. Typically, the case is easier for the government to make when they have a victim that wants to participate in the proceeding, but even when this is not the case they may simply subpoena the victim who then must appear and testify.
First things first - your friend should surrender to the warrant and get the case back on track. He should see an attorney as soon as possible to avoid being picked up on the warrant and risk spending time in jail that may be unnecessary.
Simple assault does not require hospitalization, injuries etc. If those existed, it would be aggravated assault. When "charges are pressed" it is always the state that presses charges NOT individuals. That said, if she denies that this occurred, it may be difficult to prove the case unless there was another witness. Most domestic violence cases the victim decides she (or he) no longer wants their loved one prosecuted. It is not entirely up to them. Hire an attorney.