A law firm in Scottsdale, Ariz., tested employees who hoped, with the prick of a finger, to learn if they might be immune. In Laredo, Texas, community leaders secured 20,000 of the new tests to gauge how many residents had been infected. In Chicago, a hospital screened firefighters to help determine whether they could safely stay on the job.

In recent weeks, the United States has seen the first rollout of blood tests for coronavirus antibodies, widely heralded as crucial tools to assess the reach of the pandemic in the United States, restart the economy and reintegrate society.

But for all their promise, the tests — intended to signal whether people may have built immunity to the virus — are already raising alarms.

Officials fear the effort may prove as problematic as the earlier launch of diagnostic tests that failed to monitor which Americans, and how many, had been infected or developed the disease the virus causes. Criticized for a tragically slow and rigid oversight of those tests months ago, the federal government is now faulted by public health officials and scientists for greenlighting the antibody tests too quickly and without adequate scrutiny.

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