they could have given her a field sobriety test if they had pc..
As I said earlier, public intoxication is not illegal in this state so they had no grounds for a field sobriety test when they arrested her. I suspect they didn't find the gun until they got her to the station. At that point they asked her to take a Breathalyzer and she was within her rights to refuse. So they can't charge her with something they have no evidence for.