You will file a non-resident reciprocal return for KY. Your situation is similar to the rest of the thread: you did not live long enough in KY to be a resident of KY. Your time does matter. Had you maintained a residence and lived in KY for 183 days, you would have been considered a statutory resident of KY. But you were only there for four months, and moved in and out within the same calendar year. KY cannot process a move-in/move-out within the same calendar year, so you would normally file a nonresident return for income taxable to KY.
However, if you cannot be considered a KY resident, then the reciprocal agreement with Ohio will allow you to get a full refund of the KY taxes withheld. Of course, keep in mind that all of your income will still be taxable in OH, so it could be a "rob Peter to pay Paul" situation (refund from KY to pay OH balance due).
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