Hi Daniel. Grain of salt: I'm not an expert, but just a guy who has (successfully) rented out bedrooms in two different condos I've owned as my primary residences in Austin, TX and Atlanta, GA.
With that said, it's my understanding that usually, no, there's no special permit you need in order to rent out a room in a HOUSE. You can just take some photos, list the room on Craiglist, and get cracking.
In saying the above, it's important that I'm assuming that it really is a house: a detached unit. If it were a condo, you'd need to check with your HOA and see what rules, if any, they impose on rentals. Be careful to be clear that you're talking about renting out a room in an "owner-occupied unit," not renting out the entire condo. The rules tend to be quite different (and less strict) for owner-occupieds.
The word USUALLY is also important here. My aunt and uncle own a home in Alpharetta, GA, which is much larger than they need and which has a large basement that could easily be rented out for extra income. They can't do it, because they're neighborhood association strictly forbids renting out rooms.
It's also possible, though rare, for an individual city or county to impose extra conditions. So in order to be legal and in accordance with all the possible regulations, you'll need to check (i) with the neighborhood association (if there is one), (ii) with the city if it's in city limits, and (iii) with Westchester County.
The neighborhood association, you'll have to ask directly. There should be a written document that clearly lays this out (or doesn't - in which case it's allowed). As for (ii) and (iii), my recommendation would be to go to justanswer.com and see if you can get a quick answer.
Finally, be careful about calling anything a "bedroom" if it doesn't have a window. Many states do have statewide restrictions on that.
I wish I could be more direct - but I hope this helps!
