well, animal services officer/inspector...but chickens fall under our jurisdiction, and though your issues are more about your building, in my city, if it is housing for animals, we are a division of code compliance, and code pawns it off on animal services (as does city council), making it our problem. They don't really want to deal with it. Livestock (other than poultry) techinically falls under the sherriff's department here, but if it has anything to do with animals, we are "asked" to respond. I am betting it is at least similar in your city.
As far as hearing something off, to us that means if we knock on your door, and we hear 30 barking dogs inside, we are going to want to know whats up. Same goes for birds. If you have a twelve square foot yard, and it sounds like there are 30 chickens back there, we are going to want to know why. If it sounds like five? I don't care, and am not going to waist my precious time bugging you to gain access to your back yard (which I have to have your permission for) to inspect your five chickens unless I have gotten the complaint multiple times (reguarless of how many other officers have gotten the same complaint earlier. If I don't know what calls they have responded to, I go by how many times I personally have recieved the call).
If your city is like mine, your inspectors will be like mine, and as long as your coop is basically the dimesions it is supposed to be, and your animals are healthy, happy, and not over crowded, you shouldn't have any problems.