LOS ANGELES, CA - MARCH 09: California State Assembly Member Jimmy Gomez attends Outfest's Inaugural Fusion Lab ribbon cutting ceremony and reception on March 9, 2013 in Los Angeles, California. (Photo by Vincent Sandoval/FilmMagic)

By Mary Papenfuss

Aug 20 (Reuters) - Birth certificates in California would be changed to more accurately reflect families in which parents are of the same gender under a bill passed by the legislature on Wednesday.

The bill, which now goes to Democratic Governor Jerry Brown, would allow parents to identify themselves as father, mother or parent when a child is born, a nuanced change from the current birth certificate that backers say is more reflective of growing rights and acceptance for same-sex couples.

"This bill seems subtle but I think it's going to make a profound impact on how people view each other," said the bill's author, Democratic Assemblyman Jimmy Gomez of Los Angeles.

The measure, if signed by Brown, would be the latest in a spate of actions taken by states to recognize the rights of same-sex couples.

In March, a baby in Tennessee became the first child in that state to have two women listed on her birth certificate, although one was in the spot marked "father."

In Florida last year, a judge approved an adoption of a baby girl that listed three people as parents on her birth certificate: a lesbian couple and a gay man, who was the sperm donor for the baby but sought a bigger role in his daughter's life.

California already allows same-sex couples to put their names on a child's birth certificate, offering the choices of Mother/Parent and Father/Parent, Gomez said.

The applications for the new birth certificates, which will be available in 2016, allow both parents to choose any of the three ways to identify themselves - as mother, father or simply as a parent.

"It's a recognition that families come in different compositions now," Gomez said.

The bill, backed by the LGBT advocacy organization Equality California, passed the state assembly on a vote of 58 to 15. Six members did not vote.

There were more than 15,000 same-sex couples with children in California in 2010, according to the U.S. Census.

(Additional reporting and writing by Sharon Bernstein in Sacramento; Editing by Eric Walsh)