I've tried to find a reference in a google search but none turned up.
In Ohio party affiliation is determined by primary voting.
According to this site:
Can I check my voter information online?
Yes. You may check your voter information at www.sos.state.oh.us. If you perform a Voter Information search and the information you registered is returned, then your voter registration form has been processed by your county board of elections. If your information is not returned in the search, you may want to contact your county board of elections to check on the status of your registration. You may also be able to check through your county board of elections Web site, although not all county boards have a link to the registration files.
Okay, I found the search engine. Without reposting address specifics, I still can't get it to work.
I can't get it to accept 98th street as 98, 98th, or ninety-eighth. I'd think the full zip code should be enough. But street name is a required field.
"Do not include Street Direction(N.,W.,SE.,etc) or Street Type(St.,Ave.,Ln.etc)"
http://www.sos.state.oh.us/sosapps/elections/voterquery.aspx