The lawsuit described eight occasions, which Mr. Siegel said were based upon video evidence, in which officers arrested people who were recording in public, ordered them to leave or demanded that they delete images from cameras or cellphones.

One account described the experiences of Debra Goodman, the plaintiff in the suit, who was said to have been taking a cellphone video in 2013 on the Upper West Side of Manhattan as emergency medical technicians spoke with a woman in a wheelchair and officers stood nearby. As she did so, the suit said, an officer began recording Ms. Goodman with his phone, demanded to see her identification and then arrested her. The charges were eventually dismissed by prosecutors; she is seeking unspecified damages.

In another account, also from 2013, a man named Diego Ibanez used a phone to record officers making arrests inside a subway station. Although he was about 10 feet away, the lawsuit said, officers ordered him out of the station. Mr. Ibanez responded that he would record from a different part of the platform, the suit said, and was then arrested.

As he was in custody, an officer told him that he could avoid jail if he deleted the recording he had made, the lawsuit said. The officer then tried to erase the video, but did not do so correctly, the lawsuit said, which allowed Mr. Ibanez to later recover the video, which showed him telling the police, “You can film police officers,” just before his arrest.