The Duggar case never made it into the juvenile court system, or any court system, for that matter. The alleged crimes occurred in 2002 and 2003, but the police investigation did not occur until 2006. By that time, Josh Duggar was already an adult at age 18, so the state code covering the confidentiality of juvenile records would not apply to this case.
Yea they waited until he was 18 to tell the police.