Robbery: Police's Responsibility to Investigate a Crime

My question involves criminal law for the state of: Pennsylvania

Without going into to many details... If you report, what you believe to be a crime, to the police, must they investigate?

Even if they know the crime took place, with evidence clearly showing that a window was broken and a car missing, must they investigate it?

What are the rules on when they must file a report and when they must investigate?

Is there a law, or a Supreme Court ruling, that says the police must "Investigate and Arrest"?

Thank You.

Robbery: Police's Responsibility to Investigate a Crime