Note that there are different forms for delcaring candidacy for major party, minor party, and independent candidates.
Requirements for Candidacy
The candidate must be a resident of the state (for Governor) or district (State Senator or Representative) for at least one year immediately prior to the election (OH Const. Art. II, §. 3) and must be a qualified elector of that same district (OH Const. Art. XV, § 4)
The required number of signatures for state offices can be found in the Ohio Revised Code at:
R.C. 3513.05 - Filing for candidacy through a political party holding a primary election
The Ohio Revised Code also details several offenses that may be perpetrated by voters, candidates, or election officials. The description and penalties for these offenses can be found at R.C. 3599.01 et seq.
Candidates fall under the definition of "public officers" covered by R.C. 102.02, and are thus subject to its requirements of financial disclosure.