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O.C.G.A. 4-8-5 (2010)4-8-5. Cruelty to dogs; authorized killing of dogs(a) No person shall perform a cruel act on any dog; nor shall any person harm, maim, or kill any dog, or attempt to do so, except that a person may:(1) Defend his person or property, or the person or property of another, from injury or damage being caused by a dog; or(2) Kill any dog causing injury or damage to any livestock or poultry.(b) The method used for killing the dog shall be designed to be as humane as is possible under the circumstances. A person who humanely kills a dog under the circumstances indicated in subsection (a) of this Code section shall incur no liability for such death.(c) This Code section shall not be construed to limit in any way the authority or duty of any law enforcement officer, dog or rabies control officer, humane society, or veterinarian.
That law should cover you, section (a)(2)