What's missing from the linked web site is the following statement from the instructions* for form IT1040":
"Note: If your federal adjusted gross income is greater than $12,950, the Department recommends that you file an Ohio IT 1040 or IT 10, even if you do not owe any tax, to avoid delinquency billings"
That would appear to say, you don't need to file an Ohio tax return if your income is less than $12,950. In prior years, the instructions said that explicitly ($12,250 limit in 2016). You will owe no Ohio income tax tax if your federal AGI is $12,950 or less ($10,650 for a dependent; $15,250 Married filing jointly)
*page 10 at <a rel="nofollow" target="_blank" href="
http://www.tax.ohio.gov/portals/0/forms/ohio_individual/individual/2017/PIT_IT1040_Booklet.pdf">http...>
