Vermont law uses the undefined word "person", without specifying residency.
V.S.A. ß4003 Carrying dangerous weapons
A person who carries a dangerous or deadly weapon, openly or concealed, with the intent or avowed purpose of injuring a fellow man, or who carries a dangerous or deadly weapon within any state institution or upon the grounds or lands owned or leased for the use of such institution, without the approval of the warden or superintendent of the institution, shall be imprisoned not more than two years or fined not more than $200.00, or both.
You may carry if you are a non-resident for self protection. This excludes schools, court houses, and any federally owned property. I have also heard mixed answers regarding banks, with the state attorney general's office stating you can not carry in them. I never really looked too far into it (not that we have a lot of laws), but I don't recall seeing anywhere where you couldn't do so. It's never been an issue for me, my credit union is in another state and I generally only deal with them via mail.
Again, do some research for yourself before taking mine (or anyone's) word about whether or not you'll be alright. I've never had an issue OC'ing, although I do live in the southern part, not up by the suck-hole that is Burlington. I would read up on the "Gun Control Act of 1968," and federal laws (VT isn't tough to figure out - not a felon or prohibited from owning and over 16 = good to go) yourself to make sure you'll be fine. I think owning property over here would make you a resident (or citizen?), but again I have no idea - I've never dealt with it.
If you say you're able to purchase one over here, then you most definitely would be able to carry it. If you're really in doubt, contact our AG's office. They're pretty quick with responding, and are generally correct.