The department of corrections shall examine every juvenile who is placed under its supervision to determine the type of placement best suited to the juvenile and to the protection of the public. The examination shall include an investigation of the personal and family history of the juvenile and his or her environment, any physical or mental examinations necessary to determine the type of placement appropriate for the juvenile, and an evaluation under s. 938.533 (3) (a) to determine the appropriate level of supervision and services based on the juvenile’s risks and needs. The department of corrections shall screen a juvenile who is examined under this section to determine whether the juvenile is in need of special treatment or care because of alcohol or other drug abuse, mental illness, or severe emotional disturbance. In making the examination the department of corrections may use any facilities, public or private, that offer assistance in determining the correct placement for the juvenile.