IMHO, a fake.
The Colt .25 automatic, sometimes called the 1908 model by collectors, was apparently not issued in any general way to the military, though some were purchased for the OSS and for issue to personnel needing a very concealable pistol, such as Army criminal investigators working undercover. Small numbers were purchased from Colt in WWII, and others were obtained from dealers and from police departments which had them as confiscated weapons. There is no record that ANY of these were specially marked at the time they were bought or otherwise obtained.
Harley, the picture is of the Colt .32 or .380 caliber, which was procured under contract for general officers, the OSS, and also for some other personnel, like doctors and nurses. These latter were not allowed to carry "offensive" arms, but were allowed to carry "defensive" weapons for their own protection. These, and their UNITED STATES PROPERTY marking are well known and documented (I have one).
The .25 is another story. Pate (U.S. Handguns of World War II) says that he cannot definitively prove either that any had the PROPERTY marking or that none did. He passes along stories that they were marked after the way, possibly by units which got them back from the OSS or others. I admit the possibility, but think it unlikely.
While Pate does not seem to want to be definitive, I believe that all the guns he pictures have fake PROPERTY markings. One appears to have been buffed to remove the blue, stamped with a PROPERTY marking and then Parkerized. This is indicated by the blurring of slide markings and serial number but a clear PROPERTY mark under the Parkerizing. There are other possibilities, but I smell a fake.
Others are shown with the Ordnance acceptance stamp (crossed cannons) which are completely unlike any of those used by Colt or any other manufacturer, and which would never have been approved by Ordnance.
I have been asked to evaluate one specimen of .25 Colt with a PROPERTY marking. I stated my belief that it was a fake.
So, IMHO, until proven otherwise, all, repeat, all, Colt .25 automatic pistols with UNITED STATES PROPERTY or ordnance department markings are fakes.