Lots of good information and case analysis above (I'm impressed!); my advice when asked whether one is carrying a firearm is this: "Thank you, but I prefer not to discuss such things." Lying to the cop is a criminal offense, and stony silence is offensive and will probably result in unnecessary delays. Be polite and civil, but simply say, like Bartleby the Scrivener, "I prefer not to."
If the cop demands to see your CHP, and you are carrying concealed, then you must display the CHP certificate and a government-issued ID (passport, military ID, picture ID from a state school, etc.); If you're not carrying, then you can just tell him you're not carrying; if you're carrying openly, you can say that (it's not like it's a secret, right?).
One thing you should never, ever, do, is to touch or make reference to a firearm in the presence of a cop, even if he tells you to do remove it yourself. If he insists on disarming you, make it available and tell him he can do it himself, though you do not give your consent, but you are not going to touch the gun in his presence.