I have had the policeman ask to see mine when I was stopped for a traffic infraction. I told him it was loaded in my console. He wanted to see it. So I got it out and unloaded it before I handed it to him.
I once also had a policewoman when stopped for a traffic infraction. I gave notification, she asked me where it was and to get out of my vehicle and go to rear. She said "you never can be too careful, it is for yours and my safety". She also was wearing body armor that bulged out because it was to big for her. You never know how many of those creditials are bogus.
It may be advantageous to show your CHL if stopped for another violation. At least the cop will know you are "one of the good guys" and not a felon on the loose. At my CHL renewal class 2 members stated that they were let go with a warning because they showed their CHL's.
I had LE remove my truck gun from the truck after a minor accident, unload it and give it back to me in a plastic bag with the ammo removed from the magazine (WTH). This was after I told them I was CHL and had one in the truck.
Funny thing was I had a couple of cased shotguns in the back seat that he could not care less about. I guess handguns are just evil