I believe in two theories.

1. It was a Mafia operation, but with the backing of the CIA. The CIA definitely had no problems with Kennedy disappearing from the scene. And besides, the Mafia had worked with the CIA on the plot to kill Castro and knew too much to seriously harm the CIA. So the CIA cooperated and turned a blind eye.

2. Obviously, a CIA operation in which the Mafia played a role, probably delivering the gunmen etc. In this scenario it was the Mafia cooperating with the CIA and not the other way around.

I strongly think the second theory is the most likely, if it was a conspiracy in the first place.