^^^ Yep, that's a Colt. I have one like in the photo that was my Grandfathers. Most of the old H&R 32 revolvers looked pretty similar.
By chance that isn't a .32 Long Colt? If so can you find ammo anywhere.
My GUESS would be that it's in ".32 Colt New Police", which not not the same as ".32 Colt." The former uses the same brass dimensions as 32 S&W Long, but usually has a flat-nosed bullet.
Back in those days, S&W and Colt seemed to go to great lengths to avoid acknowledging the other company even existed. It's a bit comical when you look at a Colt DA revolver-the cylinder turns the opposite direction from an S&W, the catch for the swing-out cylinder operates in the opposite direction, and the rifling actually twists in the opposite direction. Colt carried all of these design conventions up to when they ended DA production c. 2000(I haven't looked at the new DA revolvers, but would be disappointed if they weren't made this way).