For KY you would not have to file a KY return. See below for further info:
Soldiers will claim the exemption by excluding military pay when filing a Kentucky individual income tax return starting with the 2010 return. Provided the military member has no income other than military pay, he or she would not be required to file a Kentucky income tax return. The military pay exemption applies to all Kentucky military members regardless of where the member is stationed. Kentucky income tax should no longer be withheld from checks received for military pay, beginning January 1, 2010.