This is from the Ulster County Pistol Permit Unit website:
"ADDRESS CHANGE
Should you change the address listed on your permit you must come to the Pistol Permit Bureau no later than ten days after the change becomes effective. If you move to a different County within NY State, you must make arrangements to have your Pistol Permit records transferred by contacting the Ulster County Clerks Office. "
Although it only states that if you move to a different county you need to notify, you would be required to tell them you are moving out of state. This would most likely cause your permit to be revoked, unless you own a business and can convince a judge you still need your permit. (highly unlikely)