Video access has been a particular point of contention for most board members. In its lawsuit, the board said that the damage the restriction had done to its ability to function “cannot be overstated.”

“Video access, including access to a live feed, is one of the most crucial means by which the Board can effectively monitor the City’s jails; ensure DOC’s compliance with the minimum standards the Board has established; and conduct independent, confidential investigations into incidents of violence, use of force, responses to medical emergencies, and improper, potentially criminal, conduct by DOC staff,” the lawsuit says.

The mayor’s appointees to the board have also worked to diminish oversight. Dwayne Sampson, the board chairman and an Adams appointee, called unsuccessfully for the board to hold fewer public meetings with fewer people allowed to speak at them.

Critics of the administration say that the board’s lawsuit drove home how Mr. Adams had limited insight into the jails. Elizabeth Glazer, who led the Mayor’s Office of Criminal Justice under Mayor Bill de Blasio, said that Mr. Adams had tried not just to limit the board’s ability to do its job, but to snuff it out.

The lawsuit, she said, is “a signal of the complete breakdown of a relationship between a city agency and its oversight authority. It reflects what has really been an antidemocratic, almost authoritarian playbook, a kind of war on facts where first you shut the door on information and then you gaslight on the facts that are still visible.”

Adding to the unusual circumstances, the city law department, which would normally represent agencies, has informed both the Board of Correction and the Department of Correction that it would not represent either party, saying that its efforts to manage negotiations between the two would pose a conflict. Both agencies plan to hire outside lawyers.