You need to see if the basement is a legal apartment. I would check with you NY area department of housing or township and find out how it is classified. You can get fined if you do not follow the housing code and that will be no good and harder to get permission in the future.
Wise of you to ask. While I'm thinking "probably not," I suggest you investigate the housing and building codes of your town and county for converting use to liveable space. If the basement meets the minimum requirements, you may only need a certificate of occupancy, permit and/or license.