The California Fish and Game Commission classifies Tree Squirrels as a game animal and Ground Squirrels as a nongame animal. A property owner or tenant can control in any legal manner, nongame animals that are damaging property or injuring growing crops. Game animals, like the tree squirrel have a hunting season and a license may be required.
California Fish and Game Commission - Hunting Tree Squirrels and Trapping Ground Squirrels
California Department of Pest Regulation - If you are providing ground squirrel control service for hire or profit, in California, you need a qualified applicators license (QAL). Ground Squirrels Pest Control