The following pages list books having to do with the German police agencies that endangered escaping Allied airmen: the Gestapo, the Geheime Feldpolizei (GFP), the Green Police (a civilian police), and the SD. A separate page deals with collaborators.
Note that which police agency was the greatest threat to downed Allied airmen and their helpers varied depending on the nature of the German occupation. When I first visited a WWII archive in Brussels and referred to the Gestapo, I was immediately corrected by the archivist. It was not the Gestapo that tracked down airmen and their helpers, she said, but rather the GFP (the German Secret Military Police), the result of Belgium being run by a German military government. But in The Netherlands, where the Dutch were under a Nazi civilian government, it was the SD who performed this function. The leader of one Dutch escape line with whom I corresponded told me that he had never heard of the GFP; it was the SD they feared.
But in some situations, the civilian Green Police were an even a bigger danger. They spoke the local language and knew the territory, while the Germans did not.
In addition to the books listed on the sub-pages for the different types of police, there are some general works:
Williamson, Gordon, German Military Police Units, 1939-1945, London: Osprey, 1989 (Men-At-Arms Series).
I also have come across on one of the used book services the following which I have ordered:
The German Police, Supreme Headquarters Allied Expeditionary Force Europe, 1945. CDROM.