According to "2019 Kentucky Income Tax Return Nonresident or Part-Year Resident", 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 10.
On Page 10:
Modified Gross Income—Modified gross income is the greater of federal adjusted gross income adjusted to include interest income derived from municipal bonds (non-Kentucky) and lump-sum pension distributions not included in federal adjusted gross income; or Kentucky adjusted gross income adjusted to include lump-sum pension distributions not included in federal adjusted gross income.
Chart A
Your Modified Gross
If Your Family Size is: Income is greater than:
One............................. and ............................ $ 12,490
Two ............................ and ............................ $ 16,910
Three.......................... and ............................ $21,330
Four or More ............. and ............................ $ 25,750
https://revenue.ky.gov/Forms/740-NP%20Instructions%20Packet.pdf
Thanks so much for the thorough answer! I guess that means 'yes' because of my overall income even though almost all of it is not earned in Kentucky.
It's the same in most states: you have to file with any amount of non-resident state income if your total income meets certain thresholds; typically if you are required to file a federal return.