That is my concern, especially if an aggressive prosecutor is against you, or you are in Omaha. As I read it the law is not clear, but the way many prosecutors read the law these days they can find a law which makes almost any event a potential felony, even something minor like "resisting arrest" for protesting the demand to stop video taping them doing their work in a public place.
Here is what the law says: "For purposes of this section, contact with a peace officer means any time a peace officer personally stops, detains, questions, or addresses a permitholder for an official purpose or in the course of his or her official duties." To get any more vivid than that, I would suggest that we think about what the story of this particular law probably is.
I wasn't in the state when all of this was negotiated, but I imagine that this requirement to notify LEOs of a concealed handgun on your person is the result of someone objecting to allowing legal concealed handguns in Nebraska because then "officers encountering people on the street won't know who is armed!" Now, we know that this is a silly objection, because the people likely to shoot their way out of a traffic stop are probably not the types to go and get a concealed handgun permit in the first place, nor are they the types to dutifully follow the letter of the CHP statute about when they are supposed to tell the police that they are packing. Nonetheless, this is the "danger" that lawmakers were presumably trying to avoid. (To be fair, they may have been thinking that this might prevent a permitholder from alarming cops who otherwise could be surprised at the sudden sight of a gun and get someone hurt.)
With this presumed purpose in mind, it seems to me that legislators envisioned that with their law, if on a dark and stormy night an officer walks up to a car with four people in it, any of those four who is a permitholder and is carrying would announce this to the officer. The officer would then follow the procedure set out in subsection (3) of the statute and either decide to disarm the permitholder or not. If a cop disarms a permitholder, he can only do so for the duration of the contact, a.k.a., as long as it takes to finish whatever his other business is and to determine that the person isn't a threat to anyone present, that they aren't about to be arrested, and that there is no reason why their permit would be invalid. (Obviously, if you are going to jail he probably isn't going to be giving your gun back right away.)
I have not done any research into the case law, so I'm shooting from the hip here, but my bending-over-backwards-to-stay-out-of-trouble advice would be that if you are ever in a situation where you have to speak in person with a police officer about a matter that he is investigating, or if you are in any circumstance with an officer where you can't just stand up and briskly walk away, you should probably keep your hands in plain view and take the very first convenient opportunity to calmly say, "Sir, I believe I'm required to tell you that I am a CHP holder, and I am carrying today."
