he Centers for Disease Control and Prevention said it is examining the use of cycle threshold measures “for policy decisions.” The agency said it would need to collaborate with the F.D.A. and with device manufacturers to ensure the measures “can be used properly and with assurance that we know what they mean.”

The C.D.C.’s own calculations suggest that it is extremely difficult to detect any live virus in a sample above a threshold of 33 cycles. Officials at some state labs said the C.D.C. had not asked them to note threshold values or to share them with contact-tracing organizations.

Officials at the Wadsworth Center, New York’s state lab, have access to C.T. values from tests they have processed, and analyzed their numbers at The Times’s request. In July, the lab identified 872 positive tests, based on a threshold of 40 cycles.

With a cutoff of 35, about 43 percent of those tests would no longer qualify as positive. About 63 percent would no longer be judged positive if the cycles were limited to 30.

In Massachusetts, from 85 to 90 percent of people who tested positive in July with a cycle threshold of 40 would have been deemed negative if the threshold were 30 cycles, Dr. Mina said. “I would say that none of those people should be contact-traced, not one,” he said.