The question is only asking about what you did in 2020--because you are preparing a 2020 income tax return . You do not need to tell the software that you moved to the state in 2016.
If you're getting a question about moving TO Ohio, you answered something wrong previously. For tax purposes, you are probably a full year Ohio non resident.
But, how do you manage to live in TX and work in OH? For whether Ohio considers you a resident for tax purposes, See page 10 at
If you moved from OH to TX in March of 2020, then in Turbotax enter TX as your State of Residence and indicate that you lived in another state - Ohio. Then enter the date of your 2020 move.
If you lived in TX the entire year of 2020, enter Texas as your State of Residence, and indicate that you had Other State Income from Ohio.