I was browsing this forum for Weimar police unit marks and ran across this thread. Perhaps the questions have been resolved by now but, if not, I may have some clues.
The placement and format of your KP./L. mark is very similar to marks of the form S.P./X. on a number of Lugers from the police of the Free State of Saxony (not the Prussian Province). The X in these marks may be L. (Leipzig), D. (Dresden), C. (Chemnitz) or Zw. (Zwikau). Others have identified the S.P. as standing for Schutzpolizei although it may have meant Saechsische Polizei. I am not aware of a Kriminalpolizei force in Saxony but it sure seems logical.
I would like to know if you have discovered any more information about this mark.