Looks like you can carry if you're a politician:
§ 14-269.4. Weapons on certain State property and in courthouses.
....(b)(1b) A person who has a homeland security unrestricted concealed handgun
permit issued pursuant to Article 54B of this Chapter may carry a concealed
handgun in the State Capitol Building, the Executive Mansion, the Western Residence
of the Governor, or on the grounds of any of these buildings...
but not in the courthouse