Here in NC we were told in CC class to roll down the window, hand him your license and CC permit, put your hands on the wheel and state that I have a permit to carry and I have it... wherever you have it...
I've always done this with no problem...Funny thing is, just as you found out, with a CC you usually breeze right through license checks, etc...
These guys know "the good guys" are the ones that were given a permit to carry...Remember, you have been finger printed and passed an FBI background check...If you had a pimple on your record, they wouldn't have given you the permit...