A survey of New Yorkers last week found that one in five city residents carried antibodies to the new coronavirus — and in that, Gov. Andrew M. Cuomo saw good news.

If so many had been infected and survived, he reasoned, the virus may be far less deadly than previously thought. But many scientists took a darker view, seeing instead a vast pool of people who are still very vulnerable to infection.

Like the leaders of many states, Mr. Cuomo has been hoping that the results of large-scale antibody testing may guide decisions about when and how to reopen the economy and reintegrate society.

Few scientists ever imagined that these tests would become an instrument of public policy — and many are uncomfortable with the idea. Antibody tests, which show who has been infected, are often inaccurate, recent research suggests, and it is not clear whether a positive result actually signals immunity to the coronavirus.