Being born and rasied in vermont (Montpelier) I know of no gun laws other then the Federal ones ( no schools,fed buildings and 21 to buy a handgun 18 for rlfe. and so on) Other then that I know of no such law keeping you from carrying a firearm. I have searched the laws and have found nothing but here are the laws feel free to take a look.
Vermont does have a Fish and Game law much likes New Hampshires law that says you cant carry a loaded rilfe or crossbow in a car.
Transporting Firearms & Crossbows in Motor Vehicles:
A person shall not carry or possess while in or on a vehiclepropelled by mechanical power or drawn by a vehiclepropelled by mechanical power within the right of way ofa public highway a rifle or shotgun containing a loadedcartridge or shell in the chamber, mechanism, or in amagazine or clip within a rifle or shotgun, or a muzzle loading rifle or muzzle loading shotgun that has been charged with powder and projectile and the ignition system of which hasbeen enabled by having an affixed or attached percussion cap,primer, battery, or priming powder. Unless it is uncocked,a person shall not possess or transport a crossbow in or on a motor vehicle, motorboat, airplane, snowmobile, ATV, orother motor-propelled craft or any vehicle drawn by a motorpropelled vehicle.
Here is the link for that as well it's on page 19 section 3.