A connection arrangement for a mirror back supporting plate and a mirror support member in a mirror case for an automobile outer mirror assembly comprises a connecting portion of the mirror back supporting plate being held between a connecting portion of the mirror support member and a clutch member and these members being connected to each other by a connecting member. The connecting member extends through a through-hole of the clutch member and also through a through-hole of the mirror back supporting plate. After being passed through the through-holes, the connecting member is rotated 90 degrees about its axis so that it is mounted to the mirror back supporting plate. Therefore, the mirror back supporting plate and the mirror supporting member can be easily connected together.