This paper examined (1) the association between parents who are convicted of a substance-related offense and their children’s probability of being arrested as a young adult and (2) whether or not parental participation in an adult drug treatment court program mitigated this risk. The analysis relied on state administrative data from North Carolina courts (2005–2013) and from birth records (1988–2003). The dependent variable was the probability that a child was arrested as a young adult (16–21). Logistic regression was used to compare groups and models accounted for the clustering of multiple children with the same mother. Findings revealed that children whose parents were convicted on either a substance-related charge on a non-substance-related charge had twice the odds of being arrested as young adult, relative to children whose parents had not been observed having a conviction. While a quarter of children whose parents participated in a drug treatment court program were arrested as young adults, parental completion this program did not reduce this risk. In conclusion, children whose parents were convicted had an increased risk of being arrested as young adults, irrespective of whether or not the conviction was on a substance-related charge. However, drug treatment courts did not reduce this risk. Reducing intergenerational links in the probability of arrest remains a societal challenge.