In the absence of German WWII police procurement records, it's virtually impossible to confirm that a particular pistol was one of the thousands officially issued to German police units.
As you know, for most of the war, police procured pistols were stamped with the Eagle/L at the left rear of the trigger guard. Near wars end, the L was replaced by an F. However, it's been reported that some WWII commercial pistols, not just HSc's, have been recently altered with police acceptance stamping dies.
Having a complete police rig...pistol, two matching magazines and a police proofed holster is about the best confirmation today.
Never let the most important things be at the mercy of the least important.