I am positive that you must posess a License even if on private land, but if you limit your pesting to nuisance birds and Groundhogs, no one is likely to say anything to you. Use good common sense and make your own call.
Crow season does not open until June in Ohio, April and May are closed season for crows.
European Starlings, House Sparrows, and Feral Pidgeons are fair game at any time, along with nuisance blackbirds. Groundhogs are fair game except during deer gun season, same with coyote. You can blast chucks and yotes with impunity.
Squirrel season is closed, along with coons, rabbits and possums.
IF you have a coon that is causing damage, blast it and you are covered by the depredation clause. You are permitted to humanely euthanize them, as in a pill to the brain box.