This is what I found when I googled 'Shelby Ohio Municipal Code'.
The regulations are somewhat scattered, and you can find the whole thing here,
http://www.amlegal.com/nxt/gateway.dll/Ohio/shelby/codifiedordinancesofshelbyohio?f=templates$fn=default.htm$3.0$vid=amlegal:shelby_oh
the most relevant ones seem to be:
618.18 PROXIMITY OF STABLES, PENS AND COOPS TO RESIDENCES AND BUSINESSES.
(a) No person shall keep or use a stable or pen for animals, a chicken coop or a barnyard within 50 feet of any occupied dwelling house or business house, nor at any place in such manner that the same becomes offensive or that the contents thereof are discharged or run upon another's premises or into any street or lane of the City.
618.20 DISPOSING OF ANIMAL WASTES.
(a) No person shall deposit any manure from a stable, chicken coop or pen, or swill, garbage or offensive substances, within 40 feet of any occupied dwelling or place of business.
Otherwise, it seems that you have to provide the birds with food, water and shelter, have to keep the coop clean, and no cockfighting. Other than that, there don't seem to be any restrictions, although you might want to call the zoning officer to be certain.