Check your local zoning code too. I live in a fairly rural part of MD, and technically any vehicle over 10,000lbs is considered a "commercial vehicle" (regardless of use or registration) and is prohibited from being parked on any street or most small lots. To be allowed you need to be >5ac and zoned agriculture or commercial, in any of the favors of residential it is a zoning violation. One call from one of your unhappy neighbors to the city/town and you get some fines and need to find a new parking spot.
If it is a non-articulated HEMTT you should be able to get by with a class B, but more license is always better.