Under Ohio election law, you can change your political party at a Primary Election only. This is done by requesting the ballot type for the political party you wish to be affiliated with. Ohio Revised Code Section 3513.19, .20.
If you are changing your political party at the primary election, you will be required to complete a Statement of Persons Challenged as to Party Affiliation, which is a form from the Secretary of State’s office acknowledging you want to be affiliated with and support the principles of the party you select.
If you do not want to be affiliated with a political party in Ohio, you are considered to be an unaffiliated voter. An unaffiliated voter, which is identified by some people as an "independent voter", may only vote an Official Questions and Issues Ballot, if there are any present, for your precinct on primary election day. Unaffiliated or Independent voters can vote for candidates and issues in a November General Election.
In the event you refuse to complete the form required to change parties, you will be permitted to vote a provisional ballot on primary election day for the party of your choice.