Figured I'd get my $.02 worth in....
#1. It matters what state you're in. Do you legally have to?
I just got stopped for he first time since I got my permit about 3 years ago. (maybe I really am a good guy), so this is fresh in my mind.
Realistically, I don't see why it would concern an officer that you have a carry permit. I don't see why an officer should fear someone who gave fingerprints, passed an FBI background check and waited 90 days for a permit to carry a gun.
Especially when anybody in this state who can legally possess a handgun (anyone over 18 who isn't a felon, etc.) can keep it loaded in the glovebox, in the console, holstered under the seat or pretty much anywhere as long as it's "securely encased". And it seems to be a fairly common practice.
Which is as it should be, IMHO. I mean if someone is crazy enough to kill a police officer, are they really going to care about getting a permit, following any state laws or federal laws? No. They care about staying out of prison, getting the $25 for the next rock, or whatever other demons are runniong around in their heads 4 o'clock Saturday afternooon.
O.k., now I'll get down off my soapbox...
In FL, you don't have an obligation to tell an officer you are carrying, although it's recommended. If you tell the officer you are carrying, then he sees you have nothing to hide. They know when they run your tag or your license here, because a friend of mine was pulled over and the first thing the officer asked was "Where's your gun?"
In my situation I was pulled over by a sheriff's deputy in the same county I've lived in for years- I know most of the deputies are not anti-gun types, and I don't look like some punk, so I didn't really expect any problems. I was pulled over in my wife's car, with her expired tag and my NRA and GOA stickers on it. I'm sure he must have believed I might be armed. I handed the deputy my driver's license and registration, which he asked for and that was it. I got a ticket for the tag.
(Man, I wish I could remember her birthday, for more reasons than one! $70 for the county or $70 for flowers, candy and "I'm sorry" presents? Either way it's too much.)
Anyway, that was my situation. Out of state where I don't know the law in detail, or in an area that seemed really trashy I would hand over the permit with my D.L.
Especially if it was muddy or rainy outside and I was wearing nice clothes.
I was in a situation years ago with jumpy cops (not locally) before I ever had a permit (didn't even own a firearm) and I don't think it was pleasant for me or them. The main thing I remember is lots of lights shined in my face, and not knowing if there were guns pointed at me. I think there probably were. If this happens, whatever you do, move slowly and make sure they can see your hands. Fortunately, they reminded me several times in the process. Do whatever they say.