In the Ohio state tax section, you are able to input the
dates that you lived in Ohio. Turbo Tax
uses the percentage of time that you lived in Ohio and applies the Ohio tax to
that percentage of the total income.
Just to clarify- if you performed the actual work in Ohio while a
Florida resident, Ohio can still tax that income to you as a nonresident.
From the Ohio Department of Revenue: (2017 Ohio income tax instructions)
Part-year residents use the nonresident credit on the Ohio Schedule of
Credits for income earned while a resident of another state. Individuals
who earn or receive income within Ohio will be able to claim the nonresident
credit with respect to all items of income not earned and not received in Ohio.