Can you make an anonymous call? Don't specify a particular address--just ask about chickens (stress AS PETS) in a residential area.
There may not be a specific "law" on the books about chickens.
In my town, the ordinance that was cited in my violation notice (I'll get to that later) refers to things prohibited in a residential zone and makes no specific mention of chickens--there is something about "domesticated animals"--no more than 2 over 6 months of age allowed in a residentially zoned area. Where is it written I can't have pet chickens? The question is, do pet chickens fall into the category of domesticated animals? You could buy a lot of time in my town, asking them to interpret that statute...
Maybe my story will help in some way, because I was in the same boat and know the frustration, but it's a long one-I'll try to condense.
Like you, I could find no specific ordinance, or at least none that I could interpret specifically...and I just went forward and got my chicks and had my coop delivered. I went into this knowing the possible ramifications, but also armed myself with as much knowledge as possible, so that I could make a good argument for myself.
I also didn't check in with my neighbors first (gasp!). They don't check in with me when they got a large dog and decide to leave it outside all day, barking constantly, or when they hang their dead deer carcasses from the tree bordering my yard, or when they decided to feed an army of feral cats...If you have nice, friendly neighbors, by all means, let them know! But if the relationship isn't all too good to begin with and they are the spiteful type...Let's face it--it could just backfire anyhow.
I currently have 5 8-month old chickens in a very attractive, compact coop in my small suburban yard (bordering on Urban), which is completely surrounded by a 6 ft. stockade fence. Despite this, someone snitched on me to the zoning board in December (just before Christmas!). The town zoning officer issued the obligatory notice of violation which said I had to get rid of the chickens in 10 days, but I soon found out that we're lucky to have reasonable people on our zoning board, who have more important things to concern themselves with than my chickens... Hopefully the same is true in Parsippany.
After receiving the violation, I had a polite conversation with the zoning officer and the lawyer for the Zoning Board. They know I am a very responsible owner, my girls are pets, and they are MUCH quieter than the neighbors' dogs. They were much more understanding than I'd expected. I very nicely made it clear that I wanted to do the right thing, and would be eager to do anything I could to be able to keep my hens, such as applying for interpretation of the ordinance (which gives you time, at least), or a land use variance .
I asked for and was given an "extension", and was told I could keep my girls until they decide what next steps are. That was back in December... and no one has gotten back to me. Frankly, I have it on good authority that they won't, unless someone makes a stink.
Honestly, unless they just feel like being mean, there's no reason for neighbors to complain. I've been sharing eggs with them and all tell me how adorable the coop is and how they NEVER hear my hens at all...So then, who ratted us out? I don't know, but I'm enjoying every day I have my girls. I do have a friend of a friend who could take them in if I need to re-home them, heaven forbid it ever does come to that.
When I sit and think about it, it seems so very absurd that we have to fret and worry about the legality of keeping a few hens in our own backyard! And worry about the neighbors being ok with it...
Hopefully, with more and more people keeping backyard chickens, things will change and we won't have to feel like outlaws!