Yes, if a KY return for 2015 was not filed, and you have a refund coming, you can file the KY return yet.
http://www.lrc.state.ky.us/kar/103/015/040.htm You have three years from the due date of a KY return, to file and get the refund. So a 2015 due in 2016, you would have until 4-15-2019 to file the KY return and get the refund.
You cannot e-file a prior year return. So the return will need to be prepared and paper filed.
