my personal opinion, not legally speaking, I would simply provide your permit anytime asked by an on-duty officer. denying any request from an officer usually just results in more aggravation, even if you do have the right to deny the request. because after-all, if you're totally legal to do what you're doing, the only reason you could want to deny is to be a jerk an annoy the cop. if your gun is legal and you have your permit, the one action you could do to create the lowest level of stress on all parties and take the least amount of time is simply show your permit.
and legally speaking, if someone calls the police on you for openly carrying a gun, the police do have the right to detain you until you provide proof of having your permit, in which case they then have to immediately release you if you have done nothing illegal.
also legally speaking, it is illegal to carry a handgun at all, concealed or open, without having your permit on your person.
and typically, from what I have heard from friends who occasionally carry open, as long as you are acting totally normal while open-carrying in non-confrontational locations, if an officer sees you open-carrying and he recognises that you are aware of him and dont change your manner of actions once you become aware of him, they usually wont even bother asking because they probably assume you wouldnt be stupid enough to open carry a gun especially in front of an officer if you didnt have a permit for it and have the permit on you.
I have also heard from a few people who have had the cops called on them for open carrying in public, the cops often dont even ask to see your permit, they simply say "do you have a permit for that handgun?" and when the person said yes, the officer simply said ok and left, never even bothered to actually ask to see it.
hopefully this helps answer your question as well.