NEW YORK (AP) – State officials will now let married same-sex couples list both their names on their children’s birth certificates in a policy shift deeply important to many gays and lesbians.

The decision, which echoes similar provisions in states that allow same-sex marriages or civil unions, is one of many changes since Gov. David Paterson ordered state agencies in May to respect out-of-state same-sex marriages.

The state Health Department said Dec. 12 it had agreed to the change, which came after a lesbian couple who are expecting a baby filed a lawsuit. The change would apply statewide except in New York City, which is considering revamping its own birth certificate forms to accommodate same-sex couples.

Under state law, a woman’s husband is automatically deemed a parent of a child the pair conceives through artificial insemination, whether or not he is the genetic father. Same-sex couples have complained about having to jump through legal hoops to secure equivalent parental rights.

Carolyn Trzeciak and Nina Sheldon Trzeciak of Ulster County, who got married in Canada in 2006, sued last month. Nina Sheldon Trzeciak is carrying their first child, conceived through in vitro fertilization.

The couple argued they both should be designated as parents under Paterson’s directive. The governor told state agencies to make sure policies and regulations treat married same-sex couples equally, saying a recent court ruling suggests they would otherwise risk discrimination claims.

Same-sex couples may be able to secure a second parent’s rights through adoption. But having their names on a child’s birth certificate immediately gives both spouses such rights as nursery visits and information on the child’s medical condition, the lawsuit said.

“That gives them equal treatment,” said the Trzeciaks’ lawyer, Melissa B. Brisman of Park Ridge, N.J.

The Health Department said in a statement that it had been exploring how to apply Paterson’s directive to birth certificates for some time but arranged a quick resolution for the couple because the baby was due Dec. 12.

Massachusetts and Connecticut are now the only U.S. states that allows same-sex marriages; California briefly did until voters banned it last month. Some other states let same-sex couples enter into civil unions that offer some of marriage’s legal advantages.

States that allow same-sex marriage or civil unions have made provisions for birth certificates to list both partners’ names, said Susan Sommer, senior counsel for the gay rights advocacy group Lambda Legal. It was not involved in the Trzeciak case.

While the group urges couples to cement both parents’ rights through an adoption or other court order, Sommer said getting the names of both parents on the birth certificate is a great help to the children.

The Alliance Defense Fund, a conservative legal organization based in Scottsdale, Ariz., is challenging various attempts to extend spousal rights to same-sex couples in New York. In September, a Bronx judge threw out the group’s challenge to Paterson’s directive; the organization is appealing.

The alliance argues that only the Legislature, not the governor, has authority to recognize out-of-state same-sex marriages.