Two people died in separate officer-involved shootings in the East Bay on Tuesday, authorities said.

Emeryville police shot a woman along the city’s border with Oakland after officers responded to reports of a “combative theft suspect” at 12:35 p.m. on the 3800 block of Hollis Street, said Emeryville Sgt. Fred Dauer.

Just minutes after the Oakland shooting, Contra Costa County sheriff’s deputies shot and killed a man during a confrontation in Antioch. The shooting took place on Claudia Court, just north of Highway 4, at about 12:40 p.m. as deputies sought to enforce a move-out order as part of a domestic violence restraining order, according to the Sheriff’s Office.

In the Oakland incident, Dauer said officers were told by a caller that the suspect was armed with a gun and had fled the scene. Two officers reported finding the suspect in front of a storage facility on the 3400 block of Hollis. They confronted and shot the woman, who was pronounced dead, Dauer said.

Officer Johnna Watson, an Oakland police spokeswoman, said investigators found a gun in the area of the shooting.

Oakland resident Russ Whitehead said he was pulling into the storage facility to unload boxes when he saw a woman screaming and five or six officers shouting commands at her from behind a police car.

“All of a sudden there was gunfire right next to me,” he said.

Whitehead said he ducked as bullets shattered the windows of his gray Ford Focus. Because he dropped to the ground, he said he didn’t see what the woman was doing when she was shot.

Six or seven shots rang out, Whitehead said, before an officer approached his car to see if he was OK. He said he was covered in broken glass but unhurt.

“I wasn’t really scared in the moment. You either live or you die,” he said. “I’m just sorry that things like this have to happen.”

Around 7:30 p.m., more than 50 people gathered for a somber vigil at the corner of 34th and Hollis streets.

Investigators remained at the scene of the shooting a half block away, taking measurements behind police tape as people placed candles in front of a banner listing those killed by police in the Bay Area and beyond.

At the scene of the Antioch shooting, deputies made contact with the suspect, who then charged at one of them with a knife, the Sheriff’s Office said, prompting the deputy to fire his gun and strike the man an undetermined number of times.

The 29-year-old man, whose name was not released, was pronounced dead at the scene. At the time of his death, he had a no-bail arrest warrant, officials said, but they would not provide details.

Residents of the cluster of two-story tan apartment buildings, which are across the street from the new BART station construction site, said the man had mental issues and was known to police for barricading himself in his apartment for long stretches of time.

They were in disbelief that a police shooting happened in their neighborhood, and many residents were skeptical about whether deputies needed to use deadly force.

“We would like to know more about what happened because we’re concerned about this community,” said Ramona Madden, 18. “I don’t believe (the suspect) had a weapon.”

Sheriff’s spokesman Jimmy Lee would not say what kind of weapon the man was wielding when he was killed.

The shooting will be investigated by the Contra Costa County district attorney’s office, the Sheriff’s Office and Antioch police.

The Oakland shooting will be investigated by Oakland and Emeryville police and the Alameda County district attorney’s office.

San Francisco Chronicle staff writers Kurtis Alexander and Vivian Ho contributed to this report.

Kale Williams and Nanette Asimov are San Francisco Chronicle staff writers. E-mail: kwilliams@sfchronicle.com, nasimov@sfchronicle.com Twitter: @sfkale, @nanetteasimov