More than half of Washington state’s coronavirus deaths to date have struck a single Seattle-area nursing home, a testament to the virus’s threat to the already-frail elderly. A new government report captures the devastation at Life Care Center of Kirkland in grim numbers and sheds light on what went wrong.

By March 9, the virus had also spread to at least eight other nursing and assisted living centers in King County, according to a Centers for Disease Control and Prevention paper released Wednesday. Staff members who continued working while they had symptoms and who worked in multiple facilities helped the outbreak’s deadly progress, the report states.

So did short supplies of personal protective gear and items such as hand sanitizer; lack of familiarity with standards; limited testing; and “difficulty identifying persons with COVID-19 based on signs and symptoms alone,” investigators write.

The report does not name the facility, but a spokesman for Life Care Center of Kirkland, Timothy Killian, confirmed to The Post that it refers to their nursing home.

Killian said staff have been working closely with the CDC on the analysis and now meet all the standards the agency urges. He said there was no policy encouraging employees to keep working while sick and emphasized that some symptoms popped up quickly, while people were on the job. The Kirkland center is not aware of staff who went on to work at other facilities, he said.

“This is a completely unprecedented situation,” Killian said, saying that staff “had to learn on the fly” without the guidelines now offered and struggled to get crucial testing resources.

“If there is some good that can come out of our experience, we’re grateful that the CDC has been able to publish this report,” he added.

The authors of the report advise long-term care centers to be “proactive” about identifying staff and visitors who may be infected and keeping them away, including by halting visits outside “compassionate care situations.” Centers should try to spot covid-19 patients as early as possible, they say.

Investigators found 129 covid-19 cases linked to the facility: 81 residents, 34 staff and 14 visitors, according to the CDC report, which covers the period from Feb. 27 to March 9. The death toll has already climbed by a dozen since then, to 35, according to state health authorities.