Generally, the state supreme court is exclusively for appeals and holds no trials. The court consists of a panel of judges, either appointed by the Government, or elected by the state legislature or the people for a limited term. Some states use what is known as the Missouri Plan where the governor appoints a judge for a single term who must then receive voter approval for any successive terms.
Under the American system of federalism, the interpretation of a state supreme court on a matter of state law is normally final and binding and must be accepted in both state and federal courts. Federal courts may only overrule a state court when there is a federal question, which is to say, a specific issue (such as consistency with the US Constitution) that gives cause for federal court jurisdiction.
In New York and Maryland, the highest court of the state is called the Court of Appeals. (In New York, the name Supreme Court is used for a trial court.) In West Virginia, the highest court of the state is called the Supreme Court of Appeals. Oklahoma has two separate highest courts, one for criminal appeals and one for civil cases. The former is called the Court of Criminal Appeals. The latter is called the Supreme Court.
States with Partisan Elections
States with Non-partisan Elections
States with election by the Legislature
States with Appointment by the Governor
States using the Missouri Plan