It has also initiated several programs designed to improve the effectiveness of the court system. A primary function of the Supreme Court is to ensure independent, open, fair and efficient resolution of disputes in accordance with the federal and state constitutions and laws. Cases come to the Supreme Court in a number of ways: 1  A party who has lost a case in the Court of Appeals may file a petition for review. 2  Any party may ask the Supreme Court to bypass the Court of Appeals and take a case. 3  The Court of Appeals may ask the Supreme Court to take a case by certification.