Okay, so it is not proper to refer to Virginia as a state. All official documentation in Virginia refers to it as the Commonwealth of Virginia, not the State of Virginia.
However, Virginia's Commonwealth Police cars still have "STATE POLICE" emblazoned on the side, perhaps for the sake of clarity for the thousands of New Yorkers that pass through the state every day on their way to Florida, perhaps because Commonwealth Police is too many letters.
It is a quandary, though, all the same. The police cars are the only concession Virginia will make to being just like any other member of the Union, and not some special district which all other members should curtsy to.
It is my understanding that Pennsylvania, Massachusetts, and Kentucky are officially commonwealths as well, but Virginia is by far the most rabid about declaring it.