Legislation headed toward Gov. Rick Snyder's desk would protect the confidentiality of parents who give up their newborn by leaving the child at a hospital or with emergency responders.
The Safe Delivery of Newborns Law, enacted in 2000, lets parents surrender a newborn who is no more than 72 hours old.
The bill approved unanimously by the Senate Wednesday would keep intact birth certificate requirements for hospitals.
But if a newborn is surrendered under the baby drop-off law, parents would be listed as "unknown" and the child as "Baby Doe."
Supporters say the legislation would guarantee anonymity to parents and stop them from leaving newborns in public restrooms and elsewhere.
The law has led to at least 175 newborns being surrendered safely.