Twenty-eight patients and 16 employees at a Cookeville nursing home have tested positive for the coronavirus, officials said Thursday, exposing another hot spot in a region that is still recovering from a rash of deadly tornadoes.

Lee Rooney, CEO at the facility, Signature HealthCARE of Putnam, said the nursing home cared for "the sickest of the sick." He said the virus had moved through the building despite added safety precautions, including eliminating visitors on March 9 and screening employees for symptoms each time they entered.

The facility had 320 employees and patients tested for the virus earlier this week after two COVID-19 cases were identified.

The vast majority of the 44 people in that group who ultimately tested positive were "symptom-free," Rooney said, raising the troubling possibility that they could have spread the potentially deadly virus to others without realizing they had it.

None of the 28 patients who tested positive had a temperature over 100 degrees, he said.

“That’s what's scary about this right now," Rooney said. "Staff and the residents aren’t feeling sick.”

Rooney said Signature HealthCARE would open a unit dedicated to COVID-19 patients. The unit will have a separate entrance, dedicated staff and additional safety provisions.

State officials said Thursday there were 37 confirmed COVID-19 cases in Putnam County. Cookeville Mayor Ricky Shelton said that number did not include the cases from the nursing home.

“That number is going to skyrocket,” Shelton said.

Shelton urged people to heed Gov. Bill Lee's new order to stay home, reiterating that people could hurt others by spreading the virus even if they don't have symptoms.

“No one is immune,” Shelton said.

“People, even young people, are dying.”

Putnam County Mayor Randy Porter leaned on language that tied back to the community's ongoing tornado recovery efforts as he pleaded for people to cooperate.

“We don’t want you to panic, but we need you to take this serious, and some of you are not doing that,” Porter said. “We live in a great community where we care for one another, so let’s work together like we always do to stop the spread of this virus."

Porter reflected the weariness of a region that is still bruised by tornadoes that killed 19 people and leveled whole neighborhoods. He asked citizens to pray for the leaders navigating the latest crisis.

"The stress of all this sometimes, daily, is unbelievable," Porter said. "We're Putnam County strong, we're Cookeville strong and we will make it through this."

Nursing homes and assisted living facilities in Tennessee and across the nation have become hot spots for COVID-19.

At the Gallatin Center for Rehabilitation and Healing, more than 100 people — 74 residents and 33 staff — have tested positive for the virus. Dozens remain hospitalized and four residents have died.

Gentry Estes contributed to this report.

Reach Adam Tamburin at 615-726-5986 and atamburin@tennessean.com. Follow him on Twitter @tamburintweets.