After reviewing Henry's photos, I must change my interpretation of the markings. The pistol was never issued to the Gumbinnen district. With his permission, here is a photo of the marking:
The two readable markings are both from the city of Kassel in the Kassel administrative district. There was an original marking that included a "3" that may also have been from Kassel.
The first readable mark is
S.C.I.4.23. and conforms to the 1922 Schupo marking instructions. It is an early 1920s marking from the time the city's name was Cassel (prior to 1926). The pistol was weapon number 23 of Bereitschaft 4.
The second marking is
S.Ka.I.377. , conforming to the 1932 marking instructions and the revised spelling of Kassel.
The photo below shows that there is no sear safety on the pistol. This, as well as the format of the first marking indicates the gun belonged to the barracked Bereitschaftspolizei that was transferred to the military in 1933-34, before the pistol received this device.
While a very nice Luger with interesting police markings, it is not as unique as I thought and does not clear up the uncertainty in Gumbinnen markings.