Watch: 19 Kids and Counting's Joseph Duggar Arrested, Accused of Molesting 9-Year-Old Girl on VacationContent warning: This story discusses child sexual abuse. Joseph Duggar remains in police custody. Following the 31-year-old's March 18 arrest in Tontitown, Arkansas, his mugshot was posted to the Washington County Office of the Sheriff's website, where a bearded Joseph can be seen looking into the camera.