The landlord’s agent kept calling, texting and showing up at their doors, the tenants said.

He claimed that the police were investigating drug use and prostitution in the building. He warned that rents would skyrocket. He said that the building next door would be demolished — possibly theirs, too, eventually — and that conditions would become unlivable.

To the tenants, who were in rent-stabilized units and paying below-market rents, it was all an attempt to illegally pressure them to move out, an increasingly common complaint heard in New York City’s Housing Court. Usually, it is the residents’ word against the owners’, but the tenants of 444 East 13th Street, in the East Village, went to court armed with more than a tale: They had audio and video, surreptitiously recorded on cameras and smartphones, from conversations they said had been meant to scare them into leaving their apartments.

“The building is going to be shaking; the vermin will start running,” one agent, who identified himself as Newton Hinds in a cellphone audio recording, said about the planned demolition.

“It’s going to be a nightmare,” Mr. Hinds said of the supposed police investigation, this time on video.