There are multiple different rules in many locales. Here are the rule for MN (as of 20 years ago) The DNR has a season on them, so you have to have a small game license (no license needed if under 16), hunt in season, obey the maximum per day limits, and eat it after you kill it. The health department considers them rodents and will sometimes issue permits to kill them year round in specific areas, you don't need to eat them. Agriculture law allows you to kill any non-endangered species that is a pest (this is what allows you to kill mice as well).

Remember the above is MN law as of 20 years ago when I last checked. Such law changes from time to time and place to place.