Here is some info...not much out there on these...
"These are rare unusual C-prefix serial numbered pistols. Two serial ranges have been reported with the 'C-' prefix: 3-digits (121-524) and 6-digits (110092-115677).
The 3-digit serial pistols display standard 37M markings, and chamber the 9mm, so they are considered a variant of the 37M and discussed there.
The 6-digit serial pistols chamber the 7.65mm, have the thumb-safeties installed, utilize German Contract leftover P37 parts and P37 slide legend with the addition of "BUDAPEST" and the 'FFG' (for Fémáru Fegyver és Gépgyár) in a shield logo on the slide. There are no German codes, WaffenAmts etc on these pistols. The 'FFG' shield logo was used from 1938 until 1946, when FFG was nationalized and renamed to Lámpagyár (or Lampart).
One of these C-prefix P37's comes with US Military capture papers, which narrows down the possibility of manufacture/assembly to between April 1944 (completion of German contract) and December 1944 (encircling of Budapest by the Red Army). So this particular pistol was taken by its Hungarian owner out of Hungary, escaping Russian capture, and the pistol was surrendered to the US Army after May 1945 in Austria.
Please e-mail any info you know about these C-prefix P37's."
From here...
http://www.hungariae.com/FromP37.htm