None of the Glock 22s with the IL State Police are marked. They look like any other Glock 22.
The last duty guns that were marked were the 39-nothing. Might have been some 39-2 that were marked but I don't recall ever seeing any so marked. The 39-nothing will be stamped on the dust cover "ILL.S.P." followed by a number. The number is an inventory number and does not have any bearing as to which Trooper carried it. The state of IL at the time required a unique inventory number on every piece of equipment. The serial number would not suffice so the guns were stamped with inventory numbers.
Following the 39-2 the ISP issued the 439, 459, 469, 5904, 6904, Glock 22, and Glock 23. There were also some Walther PPK stainless issued to senior command. None of those were marked with any ISP identification and they all look like any other gun of those models.
You might find a shotgun stamped with IL State Police or some variation of the spelling. Shotguns would be Winchester Mod 97, Mod 12, Ithaca 37. They will be stamped in the butt stock fairly deep. It will look like it was branded on with a hot iron. I don't ever recall seeing any S&W 3000s with the markings but there could be some. I can't recall now if my issued 870 had the ISP markings or not. I removed the stock right after it was issued to me and carried it my entire career with a folding stock. When I retired the range removed the folding stock and returned it to me but I never saw the issued stock after I swapped out for the folder.
S&W made a limited run of 5904 which were ISP commemorative guns. They were stamped with the ISP seal and some gold inlay. Weren't too many sold. They were individual purchase, not dept purchase, and were meant for display. The ISP never purchased nor issued any of the commemorative guns.

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183rd FBINA