You can find the cert. petition here. From a James Madison Center press release I received via email:

Today, a judicial candidate and a North Carolina political action committee filed a petition for writ of certiorari with the U.S. Supreme Court, asking it to review the Fourth Circuit’s ruling upholding the rescue funds provisions of North Carolina’s public funding scheme. The rescue funds provision is meant to assist publicly funded candidates to fend off “excess” spending by their privately funded opponent and any independent expenditures spent against them. When privately funded candidates spend over a certain amount and when independent groups spend money against publicly funded opponent, the publicly funded candidate gets additional government funds.
In the case, Duke v. Leake, judicial candidate Judge Duke and North Carolina Right to Life Committee for Independent Expenditures Committees wanted to make expenditures during the 2006 election cycle without triggering additional government funds to that candidate’s publicly funded opponent. Duke made expenditures in excess of the triggering amount and IEPAC was deterred from making any.
In addition, North Carolina’s rescue funds provisions requires additional burdensome reports to be file by privately funded candidates and by independent spenders which are not required for publicly funded candidates.
The Fourth Circuit ruled that the rescue funds and disproportionate reporting requirements did not unconstitutionally burden privately funded candidates like Judge Duke or independent spenders, dismissing the rationale of an Eighth Circuit case, Day v. Holahan, which found such burdens on speech unconstitutional. In the recent case of Davis v. FEC, however, the U.S. Supreme Court cited Day for the proposition that a government benefit to one candidate is an unconstitutional burden on their opponent….