Cover unit with a pivotable lid for top storage compartment for vehicle

The unit (17) has a pivotable cover box lid for a cover box for accommodating a vehicle roof pivotable between open and closed positions. The cover unit can be connected to the vehicle roof so that the cover box lid is pivoted between a rest position covering the cover box and an open position exposing the cover box when the vehicle roof is displaced between the stowed position and the closed position.