The New Politics of Judicial Elections 2009-10, from the Brennan Center for Justice at NYU Law School, called Michigan's 2010 Supreme Court race "easily" the most expensive in the country, but said it couldn't figure out who paid for it:
Most of the special-interest spending in Michigan was concealed from the public, a fact that accounts for the variation in estimates of total spending. Although ads by both parties and the LEAA were blatant attempts to sway votes, Michigan’s outdated disclosure law treated them as apolitical “issue ads,” and required no campaign finance filings disclosing the amounts spent. Estimates of total spending therefore were largely based on the volume of TV ads each group ran, and estimates of what that airtime cost. It also was impossible to decipher who ultimately bankrolled independent efforts in Michigan.
Here's the story in the Washington Post.