There is not a state or federal law requiring any parent to provide health insurance to a child. If the child were under age 18, then the doctor or hospital could hold the parent responsible for the bill. Since the child is 18, he is himself responsible for his bills -- medical and otherwise.
Since you mention custody, however, there may be terms in the custody agreement that require you to provide health insurance for the child. The school he/she is attending may offer an inexpensive student health plan; make sure the plan covers services that are out-of-network and that it has at least the Affiordable Care Act limit ($2.25 million in 2012) on "essential" benefits. If the student health plan has either of those pieces missing, then it will be better to add the child to your group health plan or buy a separate plan.
A plan that only covers on-campus doctors or has slim maximum benefits would still leave you or your child holding the bag for big medical bills. Best to avoid having to choose between your retirement savings and your child's life, if he were to need a transplant to something major.
For more plain and simple answers to health insurance questions, visit Health Unsurance blog in the "related links and sources" down below.
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