Nope. You can't own them at all. The following is from the KYDFWR Turkey regs book, page 10.

"Because of potential disease problems and genetic pollution, it is illegal to possess live wild turkeys. For the same reasons, domestic or pen-raised turkeys should not be released into the wild. Due to the potential for the spread of disease, it is recommended that turkeys not be artificially fed. Providing standing corn, wheat or clover patches is a much better alternative."