Hi ! i'm in Northern New York. You only need to register your business name with the local county clerk if you plan on advertising. And you do not require special permits or inspections UNLESS you will be using Industrial Equipment or opening a shop independent from your home. Good Luck! 
this differes from county to county. Contact the Dept. of Ag. They cover what you are wanting to do. I did need an inspection and town water, If well water it had to be tested. Its called a home processor. Some counties are a no go, others anything goes, and some like where i'm at fall in the middle.
Good luck to you
I'm from Upstate NY and they require the a whole slew of things for a legal home based cake business. You are not allowed to sell cakes made from the oven you use daily...well, I don't have two ovens so I'm already out of the running. They're really serious about this too. A lady I was taking Wilton classes with got busted selling cakes from home without the proper "paperwork" and ended up getting fined thousands.
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