My own county ordinance is the same as our STATE dog laws. If you think you have no leash law in your little rural Georgia area, you are incorrect. In absence of local ordinances, the state law applies, so for your convenience, here is the part that applies to controlling your dogs as well as exceptions for penalties for harming dogs below, and a link to the Georgia State Dog Laws: https://www.animallaw.info/statute/ga-dog-consolidated-dog-laws
Fannin County and State of Georgia Dog Laws
1-3. Duties of animal owners and citizens.
(a) It shall be the duty of every owner or custodian of an animal
within the county to exercise reasonable care and take all necessary
steps and precautions to protect other people and property from
injuries and damage which might result from the animal's behavior,
regardless of whether such behavior is motivated by mischievousness,
playfulness or ferocity. Every animal shall be restrained or controlled
so as to prevent it from chasing vehicles or chasing, menacing, or
attacking persons or other animals.
(b) It shall be the duty of all animal owners to prevent their animals
from constituting a nuisance.
(c) If the owner of an animal is a minor, the parent or guardian of such minor shall be responsible to ensure compliance with all provisions of this chapter.
§ 4-8-5. Performing cruel acts on, or harming, maiming or killing 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 or her 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, poultry, or pet animal.
(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.
Fannin County and State of Georgia Dog Laws
1-3. Duties of animal owners and citizens.
(a) It shall be the duty of every owner or custodian of an animal
within the county to exercise reasonable care and take all necessary
steps and precautions to protect other people and property from
injuries and damage which might result from the animal's behavior,
regardless of whether such behavior is motivated by mischievousness,
playfulness or ferocity. Every animal shall be restrained or controlled
so as to prevent it from chasing vehicles or chasing, menacing, or
attacking persons or other animals.
(b) It shall be the duty of all animal owners to prevent their animals
from constituting a nuisance.
(c) If the owner of an animal is a minor, the parent or guardian of such minor shall be responsible to ensure compliance with all provisions of this chapter.
§ 4-8-5. Performing cruel acts on, or harming, maiming or killing 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 or her 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, poultry, or pet animal.
(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.