I doubt that anyone has bothered to study that. But it seems to me there wouldn't be any difference

There is no noticeable difference. The odds are affected by a whole lot of things, but which side of the road everyone drives on isn't one of them.

Car accident odds are affected by the traffic density and speed as well as the quality of driver training.

The UK has a higher traffic density and higher speeds than the US but a much lower accident rate.

Crash statistics are more closely related to things like how many cars are on the road and average commute time for a particular area. RHD vs. LHD have the same chances of being in an accident.