SAN JOSE — Supervisor Dave Cortese is proposing that Santa Clara County change the way it notifies law-enforcement agencies about the release from jail of violent felons, after a recent San Jose homicide allegedly committed by an undocumented immigrant.

The death of Bambi Larson, who was killed on Feb. 28 in her home in a quiet neighborhood in South San Jose, sparked local outrage, as well as criticism of the county’s policy of not notifying federal immigration authorities when undocumented immigrants are released from its jails.

Immigration and Customs Enforcement officials went further, noting that ICE agents had in the past sent the county six civil requests to detain Carlos Arevalo-Carranza, 24, the suspect in the Larson murder, when he was about to be released from jail after serving sentences for a raft of offenses, at least two of them violent. Detainer requests ask counties to hold individuals long enough for ICE to pick them up for deportation proceedings. In the case of the Larson suspect, all six were ignored, in line with county policy, and Arevalo-Carranza was released without ICE being notified.

Cortese said the modifications he’s seeking preserve Santa Clara County’s requirement that a warrant from ICE — or any law-enforcement agency — be obtained before the county will hold people beyond their prescribed jail time, and does not change the county’s overall denial of civil detainer requests.

In the proposal he announced Thursday, Cortese urges the county to work with the sheriff, district attorney, San Jose police, Office of Immigrant Relations and other stakeholders to come up with policy amendments “to ensure the timely and lawful notification to other local, state and federal law enforcement agencies, including ICE, of releases of inmates convicted of serious or violent felonies.”

San Jose Police Chief Eddie Garcia lauded the collaborative elements of the proposal and said he believes county supervisors “have the best interests of our residents at heart.” But, he said, he also didn’t want his message to get lost in the discord over warrants and detainer requests.

“No one’s asking them to detain them” beyond their release date, Garcia said, referring to jail inmates that ICE has requested be detained longer. He said they are simply asking that the county allow ICE to be notified about the imminent release of people who have committed serious or violent crimes. Notification in those cases is allowed under the state’s sanctuary law, which the county policy currently supersedes. And warrants, he noted, are not needed for those notifications to be given.

Cortese’s proposal emphasizes that all law-enforcement agencies would receive the notifications, even though ICE is presumably the only one that could make use of them.

“This is a pretty significant departure from where we’ve been, incremental as it is,” Cortese said. “Warrants or not, our immigration system is broken, but our communication system is also broken. We’re trying to fix parts we can fix without breaking any other laws.”

Another component of Cortese’s proposal would compel county officials and police departments to work with ICE to streamline the transfer of jail inmates to federal custody, in compliance with a warrant or court order, and create a system where county police agencies can get real-time notification of “ICE-initiated judicial warrants.”

After the Larson homicide, Santa Clara County officials blamed federal immigration authorities for failing to get a warrant for Arevalo-Carranza.

“When ICE was asking us to do holds on a request basis without a warrant, it was unconstitutional, and it was shot down over and over again,” Cortese said. “Their objections in the past were never absolutely clear.”

But ICE has said that the rejection of those civil detainer requests by the county has stymied their efforts to deport violent criminals who are in the country illegally. Besides the six detainer requests they said they sent for Arevalo-Carranza in Santa Clara county, they also sent three requests to law enforcement agencies in Los Angeles.

“It’s unfortunate that our communities face dangerous consequences because of inflexible state laws that protect criminal aliens,” reads a statement from ICE.

ICE officials also argue that the insistence on warrants is misguided, since the agency’s enforcement and removal operations division, which issues the detainer requests, is enforcing civil immigration violations, not criminal ones — like human trafficking — which are the domain of the Homeland Security Investigations division.

Cortese’s plan would align Santa Clara County with current practices in San Mateo County, and the proposed policy shares elements with a proposal made by Board President Joe Simitian in 2013, when the county and state were bolstering their sanctuary policies.

Police say Arevalo-Carranza, who lived in San Jose but was originally from El Salvador, broke into Larson’s house on Knollfield Way and stabbed her to death early on the morning of Feb. 28. It remains to be seen how much of an effect Cortese’s plan would have on a case like Arevalo-Carranza’s, or whether someone with a similar criminal background — which for him included drug, burglary, false imprisonment and other charges — would warrant notifications under the proposal. The arbiters of that would still be Sheriff Laurie Smith and her administrators, who supported Cortese’s proposal.

“Ms. Larson’s murderer should have been deported based on his criminal history and violent past,” Smith said in a statement.

Mayor Sam Liccardo said he hopes the latest proposal “actually results in long-overdue changes to enable jail officials to make the common-sense distinction between predatory felons — as contemplated by SB 54 — and the 99-plus percent of members of our immigrant community who would never commit such crimes.”

But Luis Angel Reyes Savalza, immigration attorney and member of the Santa Clara County Forum for Immigrant Rights and Empowerment, contends those citing Larson’s death to push policy changes are capitalizing on the tragedy ”for political ends.”

“Fixating on the individual’s alleged nationality does a disservice to the victim’s family and dangerously misleads the public with racist notions about who immigrants are,” he said in a statement.

Santa Clara County Public Defender Molly O’Neal said she also doesn’t see a need to veer from the county’s current standard.

“There is absolutely no reason ICE can’t get a warrant in any case where they believe they have probable cause to detain an undocumented individual,” O’Neal said. “We should not govern or be guided by hysteria, and the public discourse should be mindful of all guiding legal principles and the rule of law, both state and federal.”

Garcia said he is simply trying to do what he can to get criminals, immigrant or otherwise, off the streets.

“This is not hysteria,” he said. “We’re trying to close loopholes in protecting our communities.”