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Patrick Brannigan of the New Jersey Catholic Conference was unavailable to talk about Mr. Christie’s proposed law Monday, but in past testimony, he has quoted a court ruling that said adoptive parents “have an interest in having the birth records placed under seal” to permit them to raise the child as their own “without fear of interference from the natural parents.”

Open-records advocates contend that such fears are often overblown.

When such states as Delaware, Oregon and Tennessee opened their adoption records to adult adoptees, hundreds of birth parents consented to contact and only a “minuscule” number blocked release of the information or refused contact with the child, said Ms. Foster.

Other states likely to consider open-records bills this year include Pennsylvania, New York and Connecticut, she said.