In Texas, you are supposed to show them your CHL anytime you are asked for ID - like at a traffic stop.
I've been asked if I am carrying. I considered telling him it was none of his business (it isn't) but say yes if I am.
I've never had them ask to see it.
If you refuese, and if he's a bully and wants to throw his weight around he can always put you under arrest, search you and take it. Should be interesting - especially because it's against most departments policies.