my wife and i went on a capitol tour yesterday. while standing in line for the metal detector i asked the police officer what the rules were on weapons. he asked what type of weapon and i said a gun. he asked if i had a CCP, which I showed him. he asked where the gun was and i pointed to my back pocket. he said you're fine, you just can't go on the Senate floor or gallery while the Senate is in session. they were already gone for the day, so no problem. he also said that next time, dont put the gun in the xray bowl with all the keys and loose change. since they already know about it you can just keep it in your pocket/holster/whatever. then we had a chat about kel-tecs and how i liked mine. nice guy!
as for the General Assembly building, show a CCP and you are good to go.
outside the buildings, no issues.