The cause of death, the manner of death, and the mode in which the death occurred must be incorporated in the death certificate filed with the registrar of vital statistics of this state. The term “unexplained sudden death in infant or child with or without intrinsic or extrinsic factors, or both” may be entered on the death certificate as the principal cause of death only if the child is under the age of one year and the death remains unexplained after a case investigation that includes a complete autopsy of the infant at the state’s expense, examination of the death scene, and a review of the clinical history of the infant.