Virginia Motor Vehicle Code, § 46.2-819.4. Smoking in proximity to gas pumps; penalty.
Any person who smokes or uses an open flame within 20 feet of a pump used to fuel motor vehicles or a fueling tanker being used to deliver gasoline to a gasoline station is guilty of a Class 3 misdemeanor if smoking or the use of an open flame is prohibited by a sign at the pump. Any person who causes a fire or explosion as a result of a violation of this section is guilty of a Class 1 misdemeanor.
I couldn't find anything in Virginia's MVC requiring the engine to be turned off while refueling.