You should read and understand your state laws just to be sure but for the most part if you put it in a lock box and have it unloaded or place it in the trunk of the vehicle you should be fine in most if not all states.

I always carry handguns unloaded and in a lock box regardless of where I store them, this way if an officer sees that I own weapons on his computer (highly unlikely in my case) I can just point him to the lock box and they are a lot more at ease with the situation than if I pull it out of the glove box or something to show them.