ABSOLUTELY, find the carcass and call the Public Health Dep't. to find out where to take it for testing...delay no longer, for heaven's sake!! That is NOT normal behavior for a skunk; they are widely known to be one of the worst 'reservoirs' for rabies, and are frequently one of the species infected when rabies rears its ugly head.
Margo in NM, where there have been serious outbreaks of rabies in a couple of areas of my state in recent years, and who is getting rabies vaccine for her horses and mule this year, for the first time EVER.