A committee sent the measure to the state Senate on Thursday.
Parents who surrendered their children for adoption in the state would have one year from the law's passage to shield their identities.
During that period, adoptees would be able to contact their adoption agency to get non-identifying medical information.
After birth parents have had an opportunity to "opt out," an adopted adult or adoptive parent would be able to request a copy of the adoptee's birth certificate.
Opponents have fought the legislation since the 1980s.
