Legal Question in Legal Ethics in Ohio

Not necessarily. The issue is whether the Judge's friendship with the plaintiff is so strong that the Judge can no longer be a fair and impartial jurist. In large metropolitan areas, like Columbus, the Judge might be willing to decline to hear the case, simply to avoid the appearance of impropriety. In smaller counties, where there may be only one judge, when the elected Judge declines to hear the case the county has to hire a visiting judge to hear the case. This makes the elected Judge consider very carefully whether he can be fair and impartial, rather than simply declining the case out of an abundance of caution.

The neighbor can file a request to have the Judge disqualified. That request is turned over to the Chief Justice of the Ohio Supreme Court, who decides whether the Judge's relationship with the plaintiff is too close to allow the Judge to hear the case. Based only on what you wrote, I would predict that the Chief Justice would not disqualify this judge.