SACRAMENTO — Efforts to overturn a law that holds accomplices in murders as culpable as those who do the killing narrowly passed the state Assembly on Wednesday.

SB1437 by Sen. Nancy Skinner, D-Berkeley, would limit murder convictions to those who actually commit the crime, changing current law that holds accomplices to the same standard as those who actually committed the crime under what is called the felony murder rule.

The bill now heads back to the Senate, where it passed previously. If approved there again, the bill would head to Gov. Jerry Brown.

SB1437 would allow those who have been convicted as an accomplice to murder to petition a court to be re-sentenced. The bill exempts any case in which a police officer was killed.

“In California, a person can be convicted of murder and face life in prison without killing anyone or even witnessing the murder,” said Assemblyman Jose Medina, D-Riverside.

The bill was several votes short for several hours in the Assembly late Wednesday night as Skinner and other supporting lawmakers leaned on fellow Democrats to approve it. Several Democrats spoke in opposition of the bill, saying the law allows those who knowingly participate in a crime, like robbery, where a person is killed, to be held responsible for someone being killed.

“You have to hold people accountable,” said Assemblyman Jim Cooper, D-Elk Grove. “You know what you are doing. This makes no sense. How far are we going to go? What if it’s your family member laying there dead?”

Some lawmakers said the retroactive nature of the bill added to their hesitance.

“We all recognize that the felony murder rule needs to be reformed, it needs to be changed,” said Assemblyman Al Muratsuchi, D-Torrance. “We’ve all heard somewhat anecdotal examples of people who have had minimal involvement or now showing of intent to commit murder but are convicted under the felony murder rule. But this bill is not the right solution.”

“This goes too far,” Muratsuchi added.

Supporters say the bill will still allow murderers to be prosecuted. They pointed to a 2018 survey by the Anti-Recidivism Coalition and Restore Justice which found that 72 percent of incarcerated women in the state with a life sentence did not personally commit the murder. The average age of someone charged as an accomplice to murder is 20 years old.

The bill would only allow a person to be charged with first degree murder if they were the actual killer, solicited the murder or aided the killing in a way that showed a “reckless indifference to human life.”

“Victims do matter,” said Assemblywoman Lorena Gonzalez Fletcher, D-San Diego. “And victims should feel good when we put away their actual killers. But nobody finds peace when we put away otherwise less culpable individuals when someone is killed. And that has happened again and again and again.”

Melody Gutierrez is a San Francisco Chronicle staff writer. Email: mgutierrez@sfchronicle.com. Twitter: @MelodyGutierrez