Legalities aside, why would you want to?
Sometimes the answer is "because I can" (sometimes it's "because they say I can't"). Maybe one thinks the sword represents a choice of internal discipline...more likely it's about coolness or bad-assery. Most people, adults anyway, won't see those things when encountering a person carrying a sword (samurai, or otherwise) on his back... the more generous minded will think attention whore; but I think more would question the mental stability of the sword bearer. Unless, and likely even if, Tomah, Wi is a very live and let live kind of place, I wouldn't be surprised if the police were called regardless of legality.
If it's about convenience of transport to a martial arts class, I suspect the instructor would recommend other options... or, at the very least, suggest skipping the trip to the grocery store.