When a written motion is filed to recuse a justice of the supreme court, he may recuse himself or the motion shall be heard by the other justices of the court.

When a justice of the supreme court recuses himself, or is recused, the court may (1) have the cause argued before and disposed of by the other justices, or (2) appoint a judge of a district court or a court of appeal having the qualifications of a justice of the supreme court to act for the recused justice in the hearing and disposition of the cause.