Perot's vote share decreased from 1992 to 1996. Compared to 1992, Dole increased Republican margins in the Denver suburbs, as well as in the Colorado Springs area and won back Larimer County.
A similar thing happened in Georgia and Montana, but even accounting for Perot's smaller vote share, Clinton should've held all those states and added Virginia or North Carolina to his column. Clinton's underperformance is the most memorable thing about an otherwise forgotten election.
I think he probably only lost North Carolina due to his anti-tobacco stance. It was a bigger issue back then.