You left out some important information. Where do you physically work?
Are you commuting? If you meet the criteria of working there, establishing a profession there or being an owner you have NY source income and have to file a non-resident return.

Check out the instructions on the NY non-resident form. File this one first, because if you pay NY taxes you're now going to have to ammend your KY return to take the NY tax credit to the extent Ky allows.