Howdy
Theodore Roosevelt was police commissioner of New York City from 1895 until 1897. In 1896 he selected the Colt New Police revolver as the first standard issue revolver of the NYPD. While not a Smith and Wesson, this revolver fired the 32 Colt New Police cartridge, which other than the shape of the bullet, is identical to the 32 Smith and Wesson Long.
The Smith and Wesson 38 Regulation Police and 32 Regulation Police were both built on the I frame. The 38 Regulation Police fired the 38 Smith and Wesson (not 38 Special) cartridge, the 32 Regulation Police fired the 32 S&W Long. In the photo below, the revolver at the top is a 38, the revolver at the bottom is a 32. The I frame was not large enough for a six shot 38 caliber revolver, so the 38 Regulation Police was a five shooter.
View attachment 998365
I have no documentation that either of these were issued to police departments, but with names like that I find it hard to believe that they were not.