Archer's right, that it's a compact 1911 style pistol. The thing to be careful of, though, is that SIG put their own touches on the slide contours for their 1911 design. At least, I know they did on the full-sized GSRs, so I am assuming that is true for the C3, as well.
For the 5" models, the rule of thumb seems to be that leather holsters for 1911s will fit the GSRs because there is a bit more give; kydex holsters will not in general fit unless they are specific to the SIG design. The C3 does not seem to have a rail, so you need not worry about that detail at least...
I'd say find a leather holster maker who will let you return if you have problems and try an officer sized 1911 holster.