Since Vermont has a state preemption over local gun ordinances, I’m not sure how this could happen, although the article does say that the state legislature would have to vote on it so, maybe, that’s the way an exemption is granted. The City Council resolution passed 10-3. From CNN:

But most people at Monday’s city council meeting spoke out against the resolution, calling it too broad and unwarranted, according to CNN affiliate WPTZ. Burlington Police Chief Michael Schirling said most gun crime in the city involves handguns, not assault weapons, WPTZ reported.

Plus, you instantly make criminals out of anyone already owning one who lives in Burlington, or drives through the city with one in their trunk.