The novel says it was a .22 "filled with soft-nosed bullets..." That's a typical Mafia up-close assassination weapon. (In a deleted scene, that's the gun Clemenza gives to Rocco.) But in the film, the camera spends several seconds on the gun Michael uses--and the muzzle appears to be far too wide for a .22. It's at least a .38. I doubt it could be a .45 or .454. Also, though the butt was taped, it looked square at the bottom, not rounded. However, the ejector mechanism looked very much like the Webley in the photo in Stavka's link.
Why use a .38 instead of a .22? Perhaps because, as Clemenza said, he wanted to leave it "noisy" to scare off would-be good samaritans.


Ntra la porta tua lu sangu � sparsu,
E nun me mporta si ce muoru accisu...
E s'iddu muoru e vaju mparadisu
Si nun ce truovo a ttia, mancu ce trasu.