Police officials would call Ms. McRae’s search a successful “hit.” But most consent searches in Greensboro are not, especially when a stopped vehicle’s driver is black. Since 2010, officers searched blacks more than twice as often but found contraband only 21 percent of the time, compared with 27 percent of the time with whites.

The same gap prevailed when officers cited probable cause to search without permission. Officers searched blacks at more than twice the rate of whites, but found contraband only 52 percent of the time, compared with 62 percent of the time when the driver was white.

If those statistics are true, Chief Scott said, “we need to figure out how we can better serve our community in a fairer way.”

Fayetteville officials believe that they have an answer. Faced with similar data, the City Council required officers in 2012 to obtain written permission for consent searches — a requirement endorsed this year by a White House task force on policing. Since then, the number of consent searches has plummeted to about one a week. Probable-cause searches dropped by more than half.

There is a downside, Chief Medlock acknowledged. Fewer weapons are being confiscated. But because consent searches seldom turned up much contraband anyway, he said, the losses are minimal.

A Catchall Charge

Carlyle Phillips said he had no trouble with the police when he was growing up in New Jersey. And he has had none in Maryland, where he now lives. But as a student at North Carolina A&T in Greensboro, he said, he had one run-in after another. And he said he saw how routine traffic stops can become a springboard into a criminal justice system that can be hard to escape.

As a college junior in January 2010, Mr. Phillips said, he was pulled over in a predominantly white section of Greensboro for failing to wear his seatbelt — even though, he insisted, he was buckled in. He said he neither used drugs nor had had any with him. But that day, he said, he watched as the officer searching his car planted a plastic bag in it, then claimed it was evidence of drug use.