Gordon,
I want to stress I could be mistaken, I was only 14 at the time, but I was fascinated (and still am) by military and police uniforms and I always paid attention to Berlin Polizei whenever I saw them. As I said, all of the regular Polizei I ever saw standing around or riding in patrol cars wore either a gray cap the same color as their uniform or the white traffic cap.
I believe I mentioned elsewhere on the forum some time ago, I attended the Berlin police show, which was a huge event. It was held in the old Olympic Stadium. The climax was when the lights were turned out, a huge fire burned in the Olympic flame bowl and at the other end of the stadium. Everyone lit up candles that vendors sold before the show began. The police band played great German march music, and a few thousand Bepos marched in wearing shakos and boots, carrying torches. It was extremely electrifying, and very 1930's like.
I did have one personal encounter with the Berlin Polizei. A friend of mine and I went walking in the Grunewald and got lost. We found our way to the Autobahn and decided if we walked down the Autobahn we'd find our way home. We didn't get far when two motorcycle Polizei pulled up to us. They were sharply dressed in light gray leather jackets and riding breeches. I distincly remember they were riding BMW motorcycles. Needless to say, at 14, I was very nervous. The Polizei closest to us said, "Americans?" (The other fellow never spoke.) I said, "Yes," and my friend, in what I thought was a smart-assed thing to do, said, "Ja." The officer then explained, in very good English, it was forbidden to walk on the Autobahn and gave us general directions on how to get home through the woods. We, obviously, made it back safely.
I don't mean to hijack your thread, but if I could share one more story. My brother was an infantry lieutenant then, and as I mentioned they had a Bepo sister company they trained with. I remember a story he told me concerning a social event he attended. The officers were invited to a formal dinner with the Bepo officers of their sister company. Afterwards they were in the Bepo company commander's office and my brother was admiring two photographs hanging on the commander's wall. Both showed shako-wearing Polizei marching in the Olympic Stadium. One had Third Reich flags flying, the other had Bundesrepublik flags flying. The commander noticed my brother looking at the photos and came over to him. He said to my brother, "You like my photos?" and when my brother replied, "Yes," the commander pointed to an individual in both photos and said, "That's me!"