Usually illegal. Almost always very ineffective. Personally, even if you can get a permit I wouldn't bother. There's probably a reason there are few wild turkeys on your property -- it's not suitable to them.
Wild Turkeys were, up until relatively recently, endangered in the US. They were once plentiful but were a main source of food for the settlers and were hunted without regulation to the point of extinction. Raise and release programs were part of efforts to restore their populations and results were poor. Michigan, if I'm not mistaken, was the only state that reported even marginally good results -- and marginal they were, at best. Wild catch and relocation were much more effective in restoring them to areas that could support them.