According to this old Shooting Times review (cached version can be seen here):
S&W Unleashes The Night Guards
the width is 1.7 inches.
I once owned a special-edition S&W model 624 in caliber .44 Special that was about the same size as the 327.
I nick-named it "The Grapefruit", because that's what it felt like I was carrying when I used an inside-the-waistband holster.
Both the gun and I had a bit of a bulge in our mid-sections, and when they were in close proximity, concealment was an iffy thing.