If you live inside the city you are required to have your pet secured. This means that your pet is not free to roam. It must stay on your property. However in the outlying county, there are only two laws established for owners of dogs.
67-2. Permitting bitch at large.
If any person owning or having any bitch shall knowingly permit her to run at large during the erotic stage of copulation he shall be guilty of a misdemeanor and fined not exceeding fifty dollars ($50.00) or imprisoned not exceeding 30 days.
67-12. Permitting dogs to run at large at night; penalty; liability for damage.
No person shall allow his dog over six months old to run at large in the nighttime unaccompanied by the owner or by some member of the owner's family, or some other person by the owner's permission. Any person intentionally, knowingly, and willfully violation this section shall be guilty of a misdemeanor, and upon conviction shall be fined not exceeding fifty dollars ($50.00) or imprisoned not exceed 30 days, and shall also be liable in damages to any person injured or suffering loss to his property or chattels (Gunn).
So what about daylight hours? There are citizens riding bikes and walking on roads and trails every day. Often dogs will chase these people. It can be frightening and dangerous, both to the person and the pet. Pets could be injured by those who are frightened. People could get attacked, especially if showing fear, or wreck their bikes. More and more mountain bikers are being attacked by dogs in the Western US and in one case a woman needed 60 stitches after being attacked by two canines near Vail, CO. These dogs see mountain bikers as a threat to their flock. Sheep dogs are trained to fend off predators like coyotes and mountain lions, and to them, a fast moving mountain bike can look like a giant jungle cat (Trek7k).