Yes, active duty pay is not taxed in KY. If your military income was your only KY income then you do not need to file a KY state income tax return.
From Kentucky Revenue Department:
"Active duty servicemembers will claim the exemption by excluding military pay when filing a Kentucky individual income tax return. Provided the military member has no income other than military pay, he or she is not required to file a Kentucky income tax return. The active duty military pay exemption applies to all Kentucky servicemembers regardless of where the servicemember is stationed. Kentucky income tax should no longer be withheld from checks received for military pay beginning January 1, 2010."
If you have other KY income, then please make sure you checked the active-duty military box for the W-2 on the "Do any of these uncommon situations apply to this W-2?" screen that appears after you enter your W-2.
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