The Colt Police Positive revolver in .38 S&W special appears to be standard issue to uniformed police officers. Cole Phelps uses it as a patrol cop to chase Edgar Kalou and fire a shot into the air to make him stop. Strangely, it also appears as Bekowsky's sidearm in "Marriage Made in Heaven" when chasing Sabo, despite it being a Detective Special throughout the other cases. This is likely the same reason why some uniformed patrolman are sometimes seen with a Detective Special. Note the actual LAPD duty-issue weapon was a Smith & Wesson Model 15 (at the time, called a "Combat Masterpiece"), from the late 1940s all the way up to 1988, when it was swapped out for the Beretta 92F. It is identified as a Police Positive in-game due to it's identical appearance to the Colt Detective Special (albeit, with a much longer barrel), which was a snub-nosed variant of the Police Positive. In fact, the weapon seen in the game is essentially the Colt Detective Special modeled with a longer barrel.
The Colt Police Postive is depicted as the issued sidearm of LAPD officers. It can only be used while Cole is a patrol officer. Ralph Dunn and all other uniformed patrolmen are issued this revolver as their main on-duty weapons. As such, it is a common sight in game, as every uniformed officer carries one (including watch commanders). They use it when they are involved in a shootout of when firing a warning round. Occasionally, an officer can be seen carrying a .38 Detective Revolver or a Colt M1911 in lieu of the Police Positve, but most patrolman carry it. Bekowsky can be seen wielding a Police Positive at the end of A Marriage Made in Heaven, when Cole shoots Leroy Sabo. This is believed to be an animation error, as Bekowsky carries a .38 Detective Special in all of the other cases as a sidearm.