You report the net loss. This is the income that you received from your KY return: a rental loss. You will not have to pay tax, but it does seem you need to file. Here is a quote from the Instruction Manual for the KY Nonresident Return:
WHO MUST FILE FORM 740-NP—Form 740-NP must be used by full-year nonresidents who had income from Kentucky sources and by part-year residents who had income while a Kentucky resident or from Kentucky sources while a nonresident. These persons must file Form 740-NP if (1) they had any gross income from Kentucky sources and gross income from all sources in excess of modified gross income for their family size, or (2) Kentucky gross receipts from self-employment in excess of modified gross income for their family size. See Chart A on page 5. (Italics added)
The amount you received for rent constitutes gross income, while your income after your expenses are calculated in is your net income (in this case a loss). You will report the loss, and your KY return will include an attachment copy of the Federal Return including Schedule E which documents your gross amount received, minus your expenses, to arrive at your loss.
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