Anticyclonic tornadoes seem to be associated with anticyclonic mesocyclones (go figure, huh) or rotation more shallow and shortlived than can be deemed a mesocyclone. Given the nature of the westerly flow aloft over the U.S., the best instability days tends to be associated with low-level warm air advection, which is signified by a veering wind profile. This type of wind profile favors cyclonic mesocyclones/supercells. There are conditions where anticyclonic supercells are favored in cases when the wind profile is backing with height, conditions with a backing vertical wind profile tend not to be juxtaposed with higher instabiility (backing profile -> cold air advection -> not good for instability)... Now, to the south of the rear-flank downdraft in a supercell, there may be an opportunity for anticyclonic rotation to develop (such was the case May 29th in central OK), which may produce an anticyclonic tornado. This rotation tends to be relatively shallow since it isn't necessarily associated with a prolonged updraft, which means that anticyclonic tornadoes tend to be small and relatively short-lived. Of course, this is pertaining to supercells, but there could be anticyclonic tornadoes produced by mutlicells, likely courtesy of complex boundary interactions which may temporarily produce an environment favorable for anticyclonic tornadoes...
