Did Ithaca offer these guns like this one from the factory or did someone else do this?
I just purchased it.
Blued.
Extended mag.
Hunting scenes on sides.
DS Police special written on barrel.
All the blueing seems even and not mismatched.
According to the serial number it’s a 1976 model
I saw the gun for sale and couldn’t pass it up, I’ve never seen another one setup like it.

Looks factory to me.
Even saw ol' Hickok45 with one a while back -
https://www.youtube.com/watch?v=6Sz1q4mQhNk&ab_channel=hickok45

The factory DS/Police in both extended and standard length mag tubes seem to have been released with and without roll-engraved receivers as well as plain or  checkered sporter wood.  I'm not sure wwhy - but what factory had on hand at the time and/or if civilian sale model vs contract probably makes sense - however plenty of stock photos of police with roll-engraved guns.

Factory made gun.  I have one that is parkerized with the hunting scene as well.  DS Police special.  Mine has the same Raybar front sight.  I got a new replacement Raybar from Ithaca a few  months back.  I killed my first pig with that gun.

Went back and looked at your pictures again.  It has a rear sight, which mine does not.  and the stock is definitely nicer than mine.  Checkered grip with the fancy trim.  So Now IDK?  Did some police departments have better grades of trim on their shotguns?  Did someone add that stock after the fact?  Either way she is a beauty.