Professionally I'm am glad to see this post.
Too many don't realize that just because they see a YouTube video of squirrels or rabbits being shot or on the box it says that the air rifle can be used for pest control, it doesn't mean that their aren't rules and regulations that need to be followed.
In some states, there are specific laws related to nuisance wildlife while other's have none following only their hunting and trapping laws. Some require licenses (i.e., hunting license and/or trapping license if not on property you own or wildlife control license if charging a fee, etc.) while others don't. Certain states require a permit or authorization for that specific animal problem while other states are more cart blanch. Some states require that a specific dollar amount of damage be performed before any action can take place while others authorize action just for the animal being there. Then there is what can actually be done about it. For some they must live capture and then relocate the animal (i.e., in Ohio nuisance rabbits cannot be shot by any means outside of hunting season without receiving authorization by the Chief of the Division of Wildlife or his designee) while other species allow for lethal control if desired (i.e., in Ohio nuisance squirrels may be shot provided you can legal discharge a firearm/air rifle at that location).
It is important that all individuals dealing with nuisance wild animals know and understand all laws and regulations pertaining to their control. Talking with the regulatory authority for wildlife for that state will quickly educate the individual for what is legal with their specific situation.