Here in Texas we have a squirrel season... Never seen a permit. I know that in most states you can cull "nuisance" pests. Squirrels are just rats with fuzzy tails, they tear up houses, kill trees, spread disease and fleas. I have never met a nut-bearing tree owner that didn't kill as many as possible. I would think your best bet would be to call your LOCAL game warden or parks & wildlife agency and ask what the law for nuisance pest control requires. I don't think it makes a difference if you use a BB or a Barrett, its still "taking game".
Just my opinion from a thousand miles away. Use appropriate measures of salt.