Police records should be obtained when you are going to apply to ANY Visa in Panama. To make them valid they should be apostilled or legalized.
Countries that can apostille the police records can be verified in the following link:
The rest of the countries should proceed with the legalization which include the notarization of the documents and stamp at the Panamanian Consulate in order to have validity in Panama.
US citizens must acquire the Police Records from the FBI.