He removes his hand and takes a small step to the side to get a better look at House, but he doesn't ask what's wrong. Maybe he knows better. He thinks he just simply doesn't want to know the answer. If it is the hospital... Castiel will eventually be going down the same route. He doesn't want to think about that; not right now.
What he needs to do is solve this anomaly so that he can leave and get back to the war.
"Your new case - you have your... demon taking care of it?"
No one ever said Castiel was good with conversations.