Actually, the county trying to take away TM's second amendment right is at fault here. The fact that the state allows certain counties to write their own rules for what is supposed to be a right "that shall not be infringed." is at fault.
I have to totally disagree with Scout. If you were talking about a different state, then there might be an issue (i.e. an attempt to evade state taxes) then I would agree to tread carefully. However, two residential properties in the state should be no problem. The only issue that I can see would be not receiving mail notices in a timely manner. I have looked over the NY state laws, and I do not think that you will have a problem. Just make sure that, whichever address you use for your application, you also use for your driver's license and vehicle registration. Good Luck and don't carry in NYC!