The clerk of appellate courts shall submit the petition to the chief justice. The chief justice shall review the petition to determine whether the petition properly alleges facts which, if proven, constitute malfeasance or nonfeasance in the performance of official duties. If the petition properly contains factual allegations of malfeasance or nonfeasance, the chief justice shall assign the case to a special master for a public hearing. The special master must be an active or retired judge. The chief justice may issue an order denying the petition if it appears that the petition does not contain allegations which, if proven, constitute malfeasance or nonfeasance in the performance of official duties.