Gator, I'm not sure of the exact timeframe, but I believe MSP troopers were issued two-tone Model 38 Bodyguards as backups to their main revolver. I remember KY Imports selling them - they were blue guns with a stainless cylinder.
As for the main duty gun, I'm just not sure but I think they were Smith revolvers.
Check this link - in 1968 they were Model 10 HBs.
http://www.pbase.com/lowthian/image/56429145
I also found this quote on another forum, so maybe the Model 10s lasted a while:
"It used to be worse. In the late 1980s I had the opportunity to stop by a small MSP post and visit for a while. This is the era where most everyone in LE were moving from revolvers to semi-autos. The MSP rig consisted of a .38 Special 4-inch revolver, carried in a flapped, cross-draw holster. Reloads were in individual belt loops on the Sam Browne. I had seen these before, but not since the late 1960s.
Also issued to each trooper, and part of the standard duty uniform, was a 2-inch .38 Special revolver with a shrouded hammer. It was carried in a plastic holster that fit into the right front trouser pocket. When a trooper approached your car, he often had his hand in his trouser pocket. He wasn't counting his change."
http://forums.officer.com/forums/showthread.php?t=77137
Hope this helps.