The CIA did not out her. They were furious that she was outed. All signs point to Cheney. One of the first things they did was tell Richard Armitage because he was known to be a gossip. It took him weeks to repeat it.

According to Matthew Brady, Time magazine, he first heard it from Cheney and didn't regard it as very newsworthy.

After Novak outed her in his column, the Wilsons got a phone call from Bush 41 expressing extreme regret. That's how the Wilsons found out about it.