From the NYT:
Antibody testing is problematic, officials say:
Saying that the coronavirus pandemic requires an urgent response, the Food and Drug Administration has allowed about 90 companies, many based in China, to sell antibody tests that are intended to indicate whether people may have built immunity to the coronavirus but that haven’t been vetted by the government.
The agency has since warned that some of those businesses are making false claims about their products, and health officials in the U.S. and abroad have found other tests to be deeply flawed.