To my knowledge, there is not a city ordinance prohibiting the use of archery equipment on your own, private property. There is an ordinance, however, that prohibits the use of archery equipment in public parks:
97.62 HUNTING, FIREWORKS, AND FIREARMS PROHIBITED.
No person shall be allowed to carry firearms; to molest, hunt, harm, frighten, kill, trap, pursue, chase, tease, shoot or throw objects at or to set snares for any wildlife, animals, birds, reptiles and fish within the limits of any park or within 500 feet thereof except with written permission of the Department. Fireworks, firearms, "BB" guns, slingshots, pea shooters, blow guns and paint ball guns are prohibited in all park areas unless permission has been obtained from the Department. No person is permitted to practice archery or use a bow and arrow or crossbow or other similar device in any park.