For the second time, the state’s labor relations board has ruled that the city must accept mediation in its teacher evaluation talks with the United Federation of Teachers.

The board, the Public Employees Relations Board, first decided in March to heed the UFT’s request and appoint a mediator to broker negotiations about teacher evaluations in the 33 schools that until December had been receiving federal School Improvement Grants. But the city appealed the decision, arguing that it was no longer planning to negotiate a separate evaluation system for just those schools.

Now the board has affirmed its stance and once again ordered the city into mediated talks with the union.

When the board first granted the request, its director of conciliation said that because the city had not yet formally applied to switch the schools to a reform model that does not require new teacher evaluations, it was still obligated to seek a deal for the 33 schools. Today, the board ruled that the city’s bid to switch the overhaul model — to “turnaround,” in a swap that the state has not approved — “does not nullify its obligations.”

City lawyers are regrouping after the setback. “We strongly disagree with the board’s ruling and are reviewing our legal options,” said Department of Education spokeswoman Jessica Scaperotti in a statement.

The ruling is separate from the lawsuit that the UFT filed last week to stop the city from carrying out turnaround at 24 schools. But UFT President Michael Mulgrew said in a statement that PERB had supported a point that is fundamental to the union’s case.

“As we plan to tell the court at this week’s hearing, today’s PERB decision is an affirmation that the Department of Education needs to work with the teachers to find a way to improve these schools,” he said.

The Department of Education must respond in writing to the union’s lawsuit by the end of the work day on Tuesday, and the two sides are due in Manhattan Supreme Court for oral arguments on Wednesday.

In a second decision today, PERB certified the UFT as the bargaining agent for teachers at Sisulu-Walker Charter School in Harlem. The unionization bid there had been stymied by a recalcitrant board, even as the son of an anti-apartheid leader the school was named after pressed for recognition. The union represents teachers at 14 charter schools.