Because I'm obsessive:
http://codes.ohio.gov/oac/3333-1-10
It does look like you have to be living and working in OH for 12 months to establish residency.
ETA:
Things of note: "A person who has been a resident of Ohio for the purpose of this rule for at least twelve consecutive months immediately preceding his or her enrollment in an institution of higher education and who is not receiving, and has not directly or indirectly received in the preceding twelve consecutive months, financial support from persons or entities who are not residents of Ohio for all other legal purposes."
And from the utoledo website: "According to the Ohio Administrative Code, the intent of the Residency Rule is 'to exclude from treatment as resident
those persons who are present in the state of Ohio primarily for the purpose of receiving the benefit of a state-supported education.'"