I'm no legal expert by a long shot, but I know in AZ if you're in the county in an unincorporated town, like in my case Maricopa County, the county doesn't have ordinances that I know of but relies on zoning. My address is listed as Phoenix (city) and for a while I thought we were in Phoenix but that's just for the PO mail delivery when in fact we're officially in Maricopa County. When I decided I wanted chickens I initially looked to the Phoenix City ordinance that said we could keep 5 hens I believe on the first 1/2 acre, etc., but then I found out that didn't apply and we could basically keep as many as we wanted per our county zoning. So the reason I mention this is it might be the same way where you're at and perhaps there aren't any ordinances from the county in which case you're good to go as long as your zoning permits chickens (or doesn't say they're not permitted). Of course if you're in a subdivision w/HOA and/or CC&R's that specifically say you can't keep poultry then you'd run "a-fowl" of either the HOA and/or CC&R's. If it's only in the CC&R's and you don't have an HOA then it'll only be a problem if one of your neighbors under the same CC&R's decided to enforce the CC&R's.
I have other interests that don't go well with HOA's and strict CC&R's such as amateur radio (antenna's) and I learned a long time ago that just because a particular property is out in the country doesn't mean it doesn't have a HOA or strict CC&R's, so you have to do your homework before considering a place to meet your needs. Of course if we followed the letter of every ordinance, zoning allowable activities, HOA, and CC&R we'd all probably end up not doing anything but sitting in our homes and watching TV all day for fear of breaking the rules. Most properties I've looked at had CC&R's at a minimum, and almost always had at least one restriction that you couldn't do anything that would be considered a nuisance. I can't think of a rule that's more open ended than that. In your case if several neighbors nearby have chickens I wouldn't worry too much about it as long as you keep things well maintained. I would take a good look at your zoning and anything else that applied so you know what's expressly not permitted, but I'm thinking since you haven't found anything stating poultry isn't permitted that it's allowed.