I believe that the FBI issued Model 1907s during the late 30s but can't actually prove it with documentation.
Issued I'm not sure, but early DI/FBI agents definately used them, in one case took out a Barker-Karpis associate by punching through the front plate of his vest, bullet stopping on the inside of the back plate. I know in the DI days, Agents on top of their game would employ personally owned .38 Super GM's, and later, S&W Registered Magnums, but when going to war would bring along a TSMG or Remington 11 Riot. They would have picked up on the virtues of the 07 after seeing rapid but aimed single fire after getting the short end of the stick a few times. I've been trying to find out the rifle/optic combo used by Agent Winstead, that detail is just not known. I've skimmed books on FBI history, and there is just very little on specific guns, outside the .357 as a sidearm, just when researching particular investigators. But is a safe bet that this was the rifle, the FBI deployed from '33 on, probably moreso after '34, whether issued or privately owned.
The Motorized Bandits came to depend on this when the chips were down, and for the most part lead trends and use of new technology in firearms in the war on crime. It was the favored weapon of Homer Van Meter, and Baby Face Nelson used one (which I theorize, was a Lebman custom FA, as displayed today by the Tucson PD or SD, with foregrip and comp, due to eyewitness claims it was a Thompson) to kill Agents Cowley(SAC, Hoover's top guy) and Hollis. These showed up in every seized cache of savvier Depression desperadoes, and every LE inventory of note. It is often erroneously reported as being part of Hamer's team's battery in the ambush of Bonnie and Clyde (maybe it's most memorable anecdote), but in fact was not.
There was a police option from Winchester at one time, a brace of Model 97 Riot and Model 07 in one case (taken down, or not?) with pouches for shells and 10 round mags. Never heard of this one for sale, but would be a treasure if you found one. 15 round sticks were available aftermarket. Definately higher cap coming out of Lebman's shop, whether he purchased or fabricated them personally is a mystery.
This was definately the king of semi auto Police rifles/carbines for a long time, (maybe the only pure Police rifle, too, but a lot of LEOs had 94's) and people who faced a spontaneous gun battle at any moment 24/7, came to think very highly of this gun. It was the thing to have on your shoulder. Must have for any LE collection. Largely forgotten and unknown today, unfortunately, because this was the real urban carbine, THE fight winner when they happened all the time, making it the American classic that no one knows about.
C.O.'s were definately issued the 07, looks like it was common on the wall as the Mini 14 GB is today, but cannot give you specific examples of DOC's or even if the Federal system issued them.
Sorry I could not give more info. Finding it very hard to find myself. Wanted to do some writing on the 07,(and the gunsmithy of Hyman Lebman) but there's not much out there to research. I recently purchased a .401 after wanting a .351 for years (still do, b/w ammo), blown away by the old-school craftsmanship. If you get ahold of a serial number index, can you check out my 10, (306X)? I was told it was first year production. I have no use for this rifle, but still love it and want to keep it. If you get a .351 and want to shoot it, hope you are set up to reload.