Santa Clara County supervisors Tuesday refused to change a sanctuary policy that critics said allowed the county to release a violent felon, an undocumented immigrant who is accused of then breaking into a San Jose woman’s home in February and killing her.

Instead, the Santa Clara County Board of Supervisors unanimously upheld the county’s expansive sanctuary policy, saying that changing it could lead to racial profiling and problems with fair, consistent and accurate use of the policy. The board rejected a proposal to revise the policy to allow local law enforcement officials to hand over some undocumented immigrants to federal immigration authorities for deportation.

“We must separate issues of immigration status from administration of our criminal justice system and today’s decision strengthens and clarified that separation,” said Supervisor Susan Ellenberg in a statement. “Santa Clara County has long been a shining example of open and progressive thought, diversity and inclusion for the state of California and the nation.”

The development was the latest in an emotional debate that emerged in a region known for its staunch support of immigrant rights.

The county’s sanctuary policy allows the county to honor judicial warrants issued by U.S. Immigration and Customs Enforcement for the arrest of a particular individual, officials said.

The debate was ignited by the slaying of San Jose resident Bambi Larson, allegedly by an undocumented immigrant with a lengthy criminal record. Carlos Eduardo Arevalo-Carranza, 24, who emigrated from El Salvador, faces murder charges in the stabbing death of Larson in her San Jose home in late February.

ICE had previously issued nine detainers for Arevalo-Carranza with jails in Los Angeles and Santa Clara County, where he served time for local crimes. But the detainers were all ignored by California law enforcement, allowing him to get back “onto our streets to re-offend,” the agency said.

A detainer or “immigration hold” — which differs from a judicial warrant — is a written request by ICE to a local jail or law enforcement agency to detain an undocumented immigrant arrested on criminal charges for an additional 48 hours after his or her release. The intent is to give ICE time to arrest the individual and begin deportation proceedings, but some courts have deemed the tactic unconstitutional.

Many residents and local politicians had pressured the board to change its policy, which says police should not notify federal immigration authorities when an undocumented immigrant is released from jail. The policy is similar to those in San Francisco and other counties in the Bay Area, as well as a number of cities and counties across the country. But it goes beyond California’s sanctuary law, which allows law enforcement to report violent or serious criminals to ICE.

A proposal approved by the board in April, after several hours of public comment, gave county officials 60 days to work with law enforcement agencies and community leaders to craft policy amendments. Supervisors David Cortese and Mike Wasserman asked officials to consider how ICE would be notified of inmates convicted of violent felonies or other serious crimes, and would have sufficient time to obtain arrest warrants before a serious offender is released from jail.

The board’s decision Tuesday frustrated Santa Clara County District Attorney Jeff Rosen, who had challenged supervisors to push forward a more robust policy that would allow law enforcement officials to report violent or serious offenders to ICE by sending basic release information.

“This is not an immigration issue, it is a safety issue,” said Rosen. “If you are a dangerous criminal, undocumented or not, then we don’t want you here anymore.”

Supervisor Joe Simitian, like Rosen, said he fully supports the region’s immigrant communities and doesn’t believe in cooperating with ICE but that law enforcement should be able to report violent or serious criminals.

Joe White, a San Jose resident and business owner, told the board he favored loosening the sanctuary policy to give ICE more authority.

“I feel that there’s a path to citizenship, and it’s not being taken,” said White, who said he lives a few miles from where Larson was slain in her home. “I feel that if the people are being turned over to ICE, they still have a right to go to trial and go from there. I don’t think that we should not detain them.”

But dozens of immigration advocates who spoke during two hours of public comment thanked the board for its decision.

Maricela Gutierrez, executive director of the immigrant rights organization, SIREN, commended the county for its “tremendous national leadership in protecting our immigrant community and recognizing the importance of due process.”

Tatiana Sanchez is a San Francisco Chronicle staff writer. Email: tatiana.sanchez@sfchronicle.com Twitter: @TatianaYSanchez.