At least 200 people in Connecticut have been monitored for the COVID-19 coronavirus by state and local health officials since the beginning of February, Gov. Ned Lamont was told in a briefing Thursday.

Health officials asked or told the patients to remain home and away from people as much as possible for 14 days, effectively a self-quarantine.

So far, the state has tested 12 people, all showing they did not have the coronavirus strain that has led to global travel restrictions and quarantines. More were not tested because the state is using strict criteria to determine who is being tested.

The briefing, reported exclusively by Hearst Connecticut Media, was by Renee Coleman-Mitchell, commissioner of the state Department of Public Health, and Dr. Matthew Cartter, the state epidemiologist, in Lamont’s office.

“There could very well be people that have it, that haven’t been tested because of CDC guidelines,” Cartter told Lamont in the briefing, referring to the Centers for Disease Control and Prevention. Another expert told Hearst Media Thursday there is a “100 percent chance” that coronavirus cases are not being diagnosed in Connecticut because of the limited testing.

Late Thursday, Lamont’s office released a letter he sent asking the CDC to send more test kits and questioning the CDC guidelines on testing. The public health department has one kit that can test 500 to 600 people for the illness.

“I am concerned that the most recent guidelines issued by CDC cast too broad a net at this point in time and will not ensure that the right people are being tested,” Lamont said in his letter.

The CDC guidelines call for testing whenever a doctor deems the symptoms might be a sign of COVID-19, based on local patterns of the disease. “While on the surface, this approach seems reasonable, the resources available to meet this new demand are simply not adequate to ensure people most at risk get tested,” Lamont wrote.

Earlier, Lamont wanted to know why it’s taking so long to get more test kits, and he wondered why more people weren’t being tested. More kits could come as soon as next week, Coleman-Mitchell and Cartter told him.

The state is testing people who show symptoms of the coronavirus, including difficulty breathing, and who have recently visited China or another country where the outbreak is more acute, Lamont was told — a much tighter standard recommended under previous CDC guidelines.

The 200 people who are or were being monitored were identified by doctors as showing possible signs of the disease and then reported to local health departments. The status of those patients remains unclear but they were told to self-quarantine, Cartter said.

Cartter and Coleman-Mitchell did not say how many state residents are still being monitored, and how many have been under observation or self-quarantine since the tests became available last week. The late Thursday release from Lamont’s office said the CDC “advises anyone returning from China, Iran, Italy, Japan, and South Korea to stay home for a 14-day period of self-monitoring” — and said 200 state residents returning from foreign countries had been asked to self-quarantine.

But in the briefing, it was clear that the 200 also had symptoms.

At least two large medical testing companies, including Quest Diagnostics, announced Thursday they have their own COVID-19 tests and will start offering them to patients based on doctors’ orders next week.

Some health professionals are questioning why the state is testing so few people while more are being monitored.

“Based on the disease modeling epidemiologists I spoke with over the past week, I think the likelihood there are cases in Connecticut is 100 percent,” said James Hamblin, a lecturer in public health at Yale University and the author of “You’re Likely to Get the Coronavirus,” published in The Atlantic. “I would be shocked if there are not cases already...That’s not necessarily severe disease, though, and that’s the important clarification.”

Coleman-Mitchell and Cartter also told Lamont that some hospitals will set up trailers and tents outside of their buildings to test or treat possible coronavirus patients so as not to risk exposing vulnerable emergency room patients to the virus. Hospitals have been in touch with the state about how exactly they will do that, as hospital facilities are strictly regulated.

Officials told Lamont the state is advising, or will advise, that anyone with flu-like symptoms or respiratory infections should stay home and “self-monitor” rather than go to a hospital — unless they have difficulty breathing or prior respiratory conditions — in which case, they should seek medical attention.

As the COVID-19 coronavirus spreads, health officials in Connecticut and elsewhere are having a harder time identifying people to monitor, Cartter and Coleman-Mitchell said.

Staff Writer Ben Lambert contributed to this story.

kkrasselt@scni.com; 203-842-2563; @kaitlynkrasselt