Every state in the union appears to have it’s own unique set of hunting regulations. Here’s a chart that will help with figuring out what species of critter you are allowed to hunt with an air gun.
Please check with your state and local regulations, and do not rely on this chart for having up to date or accurate Hunting Regulations. Many states have rather complex rules on hunting with air rifles and even limit a hunt to certain hours of the day, or days of the week. It’s best to be informed rather than break the law and be accused of poaching.