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Honolulu Mayor Kirk Caldwell said Thursday he might allow some businesses, shut down due to the coronavirus, to open starting May 1.

They include golf courses, automated car washes and limited operations of car dealerships and real estate companies, as well as other smaller businesses, such as a piano teacher with a single student at a time, Caldwell said.

After that the next round of openings could include retail stores with ample physical distancing, pet grooming, office environments and outdoor malls.

A “high risk with modifications” category of businesses that would open later includes restaurants, beauty parlors and nail salons, and gyms. Restaurants that could be modified might pose less risk and “could actually be opened up earlier.”

Caldwell added, “We’re working hard to see what kind of things can be opened earlier because we recognize that business is struggling — they’re hanging on by the fingernails.”

Some deemed “high risk, difficult to modify” could be the last to reopen, he said. Those activities would include bars, marathons or other running races, concerts, conventions, sporting events and larger religious gatherings, he said.

Caldwell earlier announced that city parks will open starting 5 a.m. Saturday, but for active exercise only.

State Health Department officials said Thursday that Hawaii’s tally of confirmed coronavirus cases has risen to 596, up four from the previous day. The state’s coronavirus death toll stands at 12, unchanged from Wednesday.

Also Thursday, Caldwell said the city is holding off on its plan to buy 10,000 coronavirus test kits from a Texas-based company after state Health Director Bruce Anderson voiced strong objections about the product.

Only two days earlier, Caldwell had announced that the city was spending $2 million to have Everlywell provide the “fast-testing” kits as early as next week to up to seven Oahu community health centers that cater largely to underserved communities. The city had been assured that test samples to be sent to the mainland would be able to draw results within 48 hours, he said Tuesday.

“The Department of Health yesterday informed us that it is objecting to the city doing this,” the mayor said Thursday at a news conference. “We strongly disagree with the Department of Health on this, but we will be holding off for a short period … so that we can discuss this with the Department of Health before proceeding.”

Anderson’s letter suggested using the tests could expose the city to liability issues.

“The Everlywell test appears to lack (Federal Drug Administration) emergency- use approval. FDA has informed us that tests that do not have EUA cannot be used within the United States,” the letter said.

“Additionally, there is no information on the accuracy of this test, presenting significant liability issues for Honolulu and the healthcare providers that collect these specimens,” Anderson wrote.

Anderson also noted that there are “validated and approved” tests being conducted by local laboratories that the city could use.

Late Thursday, Health Department spokeswoman Janice Okubo said Anderson has since corrected himself and acknowledged that Everlywell would be using an FDA-approved lab.

“We are going to be working with the City and County on this to come up with a plan that works for everyone,” Okubo said.

Caldwell said Thursday that Austin, Texas-based Everlywell has provided coronavirus test kits to Los Angeles as well as other municipalities.

City Enterprise Services Director Guy Kaulukukui said the city had not yet signed a contract with Everlywell and that no money had been spent. “We have pushed the pause button,” he said.

Kaulukukui said the claim that the Everlywell tests cannot be used in the U.S. is incorrect. “That’s my assessment of what is allowable by the FDA, from the FDA website,” Kaulukukui said. “I think we are on the same page as the FDA with respect to what sort of tests and what level of scrutiny the tests need before they can be used in this country.”

Kaulukukui said he and other city officials spoke with DOH epidemiologist Dr. Sarah Park about the program a week and a half ago, and she raised objections. The city went ahead anyway because “no evidence was actually offered as to why the test was unacceptable,” he said, adding that L.A. officials voiced no concerns about the test’s validity or the amount of time it took to obtain results.

Asked why Kaulukukui, the director in charge of the city’s entertainment venues and the zoo, was tasked with overseeing the coronavirus testing effort, Caldwell said some of his department heads are less busy than others due to the coronavirus outbreak, adding that “he is an excellent businessperson.”

Dr. Frank Ong, Everlywell’s chief medical and scientific officer, wrote to Anderson on Thursday insisting that the health director’s correspondence to Caldwell included “inaccurate” information.

“There are no ‘FDA approved’ tests for COVID-19 at this time,” Ong said. “Rather, the FDA is authorizing tests for COVID-19 through the FDA’s Emergency Use Authorization (EUA) framework.”

“Our laboratory partners have submitted their validation data and reports to the FDA and are operating under the FDA’s Emergency Use Authorizations for these tests,” Ong said.

As for the tests’ accuracy, Ong said in an email, “The false negative rate for COVID-19/SARS-CoV-2 at our partner labs is under 3%, which is in line with the national averages for COVID-19 diagnostic testing.”