This is a peaked cap for Officers of the German Volunteer Fire Department (FFW). This dark blue wool cap is made in the saddle form top style called a Schirmmutze. The alternate round top shape looks like a plate so it is called a Tellermutze. German Fire Department piping is bright carmine so this cap is piped in that color. This bright carmine color will react to a black light and will show florescence by glowing and this is correct with WWII period Feuerwehr (FW) piping. The band is black velvet on this example and the cap cords are aluminum. Some FFW Officer cap cords will be found that have black or red flecks in them as well.
This cap has the orange color oilcloth lining normally seen on NCO caps and the celluloid sweat shield has no maker but is instead marked "Wasserdicht" indicating it is water proof. A perfectly practical marking for a Feuerwehr cap that is guaranteed to get wet. There is no maker indicated. The insignia consist of a proud Officer style Nationale cockade and a three dimensional one-piece Officer style proud police eagle. This leads me to believe this was either a low cost Officer cap or one worn by a Portepeeunteroffizier with the rank of Meister. Meisters were senior NCOs who were authorized to wear an Officer Portepee on their swords and Officer cap cords on their peaked caps.
Notice the attached Knotel uniform plate showing the blue uniforms of the NS Zeit Volunteer Fire Department (FFW) as opposed to the Professional Fire Departments which operated as full time Civil Service organizations. These police uniform plates were issued as a book or as postcards which could be collected by the public from the German Post Office.