“Consent is a tricky thing, because sometimes the police don’t make it seem like you have much of a choice,” Professor Cunningham said. Many people do not know that they have a right to decline, or would be reluctant to exercise that right, he said.

The police are required to give anyone whose property is taken a voucher, a form that serves as a receipt. Investigators are permitted to keep the phone until the case is completed if they obtained it consensually or through a subpoena, Mr. Cunningham said.

In 2009, Police Commissioner Raymond W. Kelly issued an order making clear that officers cannot demand to view photos or video footage without consent, barring “exigent circumstances.” Investigators prefer to download the video themselves, rather than rely on an individual to e-mail or copy the file for them. The reason, Mr. Cunningham said, has to do with the chain of custody.

“If you have a civilian pulling the video off and e-mailing it, then later on down the road, if the case goes to trial, the defense may raise questions about the transmission,” Mr. Cunningham said.

One of the witnesses who said his phone was taken on Saturday, Julian Miller, was with a friend in Times Square when he noticed the early stages of the confrontation.

“My friend was like, ‘You have to record this,’ ” said Mr. Miller, 22, who was visiting from Boston.

And he did. He ran after the police and the man, as his phone recorded every second of the encounter, including the moments in which Mr. Kennedy was shot to death, Mr. Miller said.