The gunman’s sister is afraid.

Naomi Alexis wants to talk about the day her 34-year-old sibling, Aaron Alexis, opened fire at the Washington Navy Yard, killing 12 people and injuring five others before being fatally shot by police. It’s time, she says, for someone in her family to open up about the mental health problems that enveloped her brother before his rampage. But she delays one scheduled interview after another.

“It’s very scary for me, now that the time has come,” she writes in an e-mail explaining her change of heart. “I don’t want to feel out of control. People died. There’s a tremendous amount of grief and pain wrapped up in all of this.”

On the morning of Sept. 16, 2013, the Alexises joined the tiny, but ever-expanding, group of families across the United States with a relative who committed a mass shooting. Their ranks include the Lanzas and the Loughners, the Holmeses and the Hasans, the Chos and the ­Harrises — names that dominated news cycles after other mass shootings.

Most families release a brief public statement expressing shock and sorrow immediately after the killings, then retreat as quickly as possible from the glare of public scrutiny. The burden of their guilt and grief and fear silences many for years and sometimes permanently.

Data collected by Mother Jones looking back at the weapons used in the last 30 years of mass shootings in the U.S. show that legal weapons are the norm.

It took five years for the parents of Dylan Klebold — one of two Columbine High School seniors who killed 12 schoolmates and one teacher and injured many more before taking their own lives in 1999 — to give an interview to the New York Times about their struggle to understand their son’s actions and live with the consequences. The parents of Eric Harris, Klebold’s partner in the Columbine massacre, have never spoken publicly.

The stigma can be relentless. Or as Naomi Alexis puts it in an e-mail: “I’ve had people stop returning e-mails, phone calls once they Googled my name.”

‘My heart is broken’

Eight hours after the gunman stalked Building 197 with a Remington 870 shotgun and sent hundreds of panicked Navy Yard workers into the streets of Southeast Washington, his name and image flashed across television and computer screens: Aaron Alexis.

The news sent a wave of reporters to the tree-lined street in Brooklyn, home to his mother, Cathleen Alexis. Yellow police tape blocked off access to the brownstone where she lived.

Two days later, as details emerged about her son’s troubled mental state, she made her only remarks about the shooting. Flanked by two clergy inside her living room, she read aloud a statement to a pool reporter.

“I don’t know why he did what he did, and I’ll never be able to ask him why,” she said in a voice that quivered with sadness. “Aaron is now in a place where he can no longer do harm to anyone, and for that I am glad. To the families of the victims, I am so, so very sorry that this has happened. My heart is broken.”

After renouncing her son’s actions, Cathleen Alexis withdrew. But the photographers, cameramen and reporters camped outside her home did not. The New York Daily News even snapped a photo of her answering her door.

Cathleen Alexis, center, mother of Navy Yard shooter Aaron Alexis, answers her door at her home in Brooklyn on Sept. 17, 2013. (Anthony DelMundo/New York Daily News)

“Random people were dropping off letters, people who pretended they knew my brother,” recalled Naomi Alexis, 32. “It was a scary thing.”

Her mother later moved out of her home in search of more privacy, she said. Since then, she and the rest of the Alexis family have been silent.

This month, Naomi Alexis agreed to meet a Washington Post reporter for an interview at a coffee shop. She said she felt it was time to talk about her brother and the mental health issues his killings raised. Aaron had been depressed, sleepless and hearing voices in the weeks before the shooting but hadn’t lost his security clearance.

On the morning of the interview, she canceled and offered to talk by phone. Eventually, her willingness to answer questions was reduced to a few e-mails, texts and very brief phone calls.

There are an increasing number of families grappling with the fallout of a mass killing committed by one of their own. According to a Texas State University study that examined the nation’s “active shooter events” — in which one or more persons killed or tried to kill “multiple” people, including at least one unrelated person — the number of these shootings went from about one every other month between 2000 and 2008 to more than one a month between 2009 and 2012, or almost 16 a year. In 2013, there were 15 mass shootings, said the study, which was posted on the FBI’s Web site.

Naomi Alexis’s reluctance to speak mirrors the response of the family of Seung Hui Cho, the Virginia Tech gunman who killed 32 people before shooting himself in 2007. After their son’s rampage, the Chos released a statement expressing their deep sorrow, but they never gave a media interview. The Chos did speak to a panel appointed by then-Gov. Timothy M. Kaine (D) to investigate the Virginia Tech shootings.

Wade Smith, the North Carolina attorney who helped Cho’s immigrant parents and his Princeton-educated sister, Sun-Kyung Cho, craft their public statement, said media outlets have continuously asked for interviews with the family, but he has turned them down at the daughter’s request.

Sometimes, Smith asked Sun-Kyung Cho how her parents were faring, because they had told him they would live in “total darkness” forever.

“The daughter would say they were doing about the same. We never went any further than that,” said Smith, who assisted pro bono. “I think the sister has managed somehow to move on with her life.”

Some parents of high-profile shooters do speak in the wake of the killings.

Peter Lanza, the father of Adam Lanza, who fatally shot his mother and 26 first-graders and educators at Sandy Hook Elementary School in Newtown, Conn., in 2012, gave a lengthy interview to the New Yorker’s Andrew Solomon.

“How much do I beat on myself about the fact that he’s my son?” said Lanza, who contacted Solomon as the first anniversary of the shooting approached. “A lot.”

Peter Rodger, the father of Elliot Rodger, the 22-year-old who in May killed six people and injured 13 others near the University of California at Santa Barbara campus, agreed to an interview with ABC’s Barbara Walters in late June and with The Post in August.

“I felt it was my duty to put out Elliot’s story and tackle the mental health element,” explained Rodger, 49, whose son made a series of chilling videos and wrote a lengthy manifesto before the rampage and took his own life at the end of it.

Since the attacks, Rodger has launched a Web site, Askforhelp.org, which provides information on mental health organizations, and offers readers a place to share their own stories about their hurdles in tackling mental health. Rodger, who directs commercials, told The Post that he often wonders if other parents of shooters experience what he goes through.

“I think about them a lot, because I am sure they’re in hell,” he said. “I understand other families are in absolute turmoil and feel the terrible guilt that we feel collectively. There’s not many of us. We’re victims as well.”

‘The grief I feel’

Before she bowed out of doing a formal interview, Naomi Alexis expressed hope that organizations such as the National Alliance on Mental Illness receive adequate funding and that police and government agencies “do a better job of responding to the symptoms of crises.”

“Mental illness has a tremendous impact on the people who live with and care for its sufferers. Mental illness isn’t a weakness,” Naomi wrote in an e-mail. “Allowing it to consume you and negatively impact your life and the lives of the people around you is. Diagnosis, treatment and maintenance should not be done in shame or secret.”

She said she hopes the families of her brother’s victims are healing.

“The grief I feel for their suffering is palpable. The guilt, at times, paralyzing.”

Jennifer Jenkins contributed to this report.