JW gave you some good advice. CT's game agency seems to be called DEEP. Call the Game Warden. They enforce the laws and will know them best. I was able to find a season summary and Woodchuck sheet on their website (see links below). It looks like CT requires a Hunter Safety course to obtain a hunting license but you can complete that online. CT does not appear to have a caliber restriction on airguns but check with the Game Warden. When you speak with the warden, explain that this is on your own property and the woodchucks are destroying your garden and are a nuisance animal. There may be some additional exceptions in that situation. Good luck and let us know how it goes.



https://portal.ct.gov/DEEP/Wildlife/...ith-Woodchucks

https://portal.ct.gov/-/media/DEEP/h...nsummary20.pdf


Edit--I would strongly advise you to research CT's Dangerous Weapons law (Section 53-206). Apparently CT regards BB guns (which would include air guns) as dangerous weapons and has restrictions on carrying/transporting them in public and specifically in a town. You may want to check with your local police department on this. And I thought CA was restrictive.

https://codes.findlaw.com/ct/title-5...ct-53-206.html