I joined the CHP in 1980. As cadets, we were issued the Model 67 (4"-barrel revolver) or the Model 68 (6"-barrel revolver). Both capable of the .38 +P+ ammo. We selected either one, I went with the Mod. 68. The pistols were stamped "CHP" on the frame. What we were told by our weapons instructors at the time is that prior to the time when the CHP started issuing these guns, officers were allowed to carry either .38 or .357 revolvers. The 2 most popular were S&W and Colts. When the CHP started issuing a specific revolver and basic ammo, they went with one firearms company (basic state-mandated bidding process) and one cal. ammo for bulk purchase (also though bidding process). The CHP weapons staff evaluated all proposed firearms and ammo under specific criteria of performance and safety. The one "political rule" was they could not call the ammo "hollow point bullets", probably because it sounded too cruel. So they labeled it "Controlled Expansion" rounds. There was no issue about whether the higher powered ammo would hurt too much. We were trained to hit center-mass for maximum effect and maximum chance of hitting the target. Deadly force is just that!
Regarding the use of .38 Cal. instead of .357 Mag., my understanding (from my instructors) is that it was an issue of ammo interchangeability. That is, in a fire fight, if an officer ran out of ammo, their partner could provide one of their speed-loaders full of the same ammo that would fit. Both .38s and .357 could take the .38 ammo, whereas only the .357s could use .357 magnum ammo. So the .38 won out. Granted, this was a rather far-fetched rationale, but it sort of makes sense.
While on the job, I noticed that even though the CHP issued the S&Ws, many officers purchased and carried their own sidearms while still using the required issued .38 cal. ammo. The CHP eventually lifted their restriction on .38 Cal. ammo, only - around 1988, I think. I purchased and carried a S&W Mod. 686, .357 Magnum and carried .357 Mag. ammo in it, which the CHP provided. This was in the days before the CHP went to automatic pistols.