Can a 17-year-old be charged with a crime for leaving their parents' home without permission in Missouri?

No. The parents can file an absentee minor report with the local authorities and then request the court to issue and order to have the minor returned to their custody or the custody of the state. If a court order of any type relating to the minor, then the order itself enables authorities to take the underage person into custody and remand him or her to juvenile authorities.