BB62 the Code of Virginia 18.2-308 defines the carrying of certain concealed weapons (including handguns) as a crime, however it provides an affirmative defense to the commission of this crime if the guilty person has been issued a valid concealed handgun permit.
18.2-308.01 provides the requirements for the carrying of a concealed handgun with the valid permit. The authorization to carry said handgun is addressed in part C of this law. In this particular instance, certain restrictions on the carrying of a concealed handgun are limited to those provided by the law and those restrictions placed by private property holders.
Code of Virginia laws in the 15.2-915 series address the limits on the control of firearms by authorities and local government agencies. The notable portion regarding the carrying of handguns is found in 15.2-915 specifically.
Now with regard to the control of the public's possession of firearms in state agencies there are a handful of Attorney General Opinions related to this, which may be somewhat related to the overall discussion. However, these are simply opinions. (Examples are Jerry Kilgore opinion related to carrying of concealed handguns in state parks, Bob McDonnell opinion related to the open carry of concealed handguns in state parks, Ken Cuccinelli opinion related to handgun carry in state colleges and universities, etc.)
It is my understanding that the governor believes his power to control the un-concealed carrying of handguns in state facilities comes, at least in part from Code of Virginia 2.2-123; however, it would seem to me that this authority as defined here would be incomplete for what he is attempting to do.
This is just a starting place based on what I can recall from memory, but I hope it helps. (
http://law.lis.virginia.gov/vacode )