(1) A voluntary relinquishment is not valid unless the parent specifically relinquishes custody of the child to the department, a licensed child-placing agency, or a specifically identified prospective adoptive parent and:
(a) the department or agency to whom the child is being relinquished has agreed in writing to accept custody of the child until the child is adopted; or
(b) the identified prospective adoptive parent has agreed in writing to accept temporary custody and to provide support and care to the child until that person's adoption petition is granted or denied.
(2) A voluntary relinquishment of a parent's rights solely to the child's other parent does not relieve the parent executing the relinquishment of any duty owed to the child or for the child's support.