Upon completion of the medical investigation under section 5823, the department shall promptly make a determination of medical eligibility. If the department determines that the child or youth with special health care needs is medically eligible for services under this part, the department shall perform a financial assessment to determine cost sharing responsibilities. The department shall authorize the transportation of an eligible child or youth with special health care needs to a provider of services approved and designated by the department. In consultation with the family, the department may facilitate transfer of a child or youth with special health care needs to a provider for treatment better adapted to the child's needs. In making referrals under this part the department shall not discriminate against health professionals qualified to render care.