ALBANY — Assemblywoman Catherine Nolan kept her promise to question UFT President Michael Mulgrew with the same tenacity as when she interrogated Mayor Bloomberg on Monday.

Nolan chastised Bloomberg for his role in New York City’s failure to reach a teacher evaluation deal, which will likely cost the city $240 million in state school aid.

Today, she told Mulgrew, “This is the fault of labor and management together.” Nolan chairs the Assembly’s education committee and usually sympathizes with the union on education issues.

“It is unbelievable to me that this union, with its great history, could not negotiate this deal,” Nolan added as she questioned Mulgrew, whose testimony before the legislature was supposed to be about the 2013-2014 state budget but focused instead on the failed evaluation deal and issues surrounding upcoming assessments aligned to new standards.

Mulgrew and Chancellor Dennis Walcott, whose testimony earlier in the day generated less confrontation, both told the legislature that they are open to resuming negotiations. Walcott even conceded that a misunderstanding could have fueled one major issue preventing a deal.

Walcott told reporters after his testimony that discussions would revisit the city’s interpretation of a “sunset clause” that the union wants to include in the deal.

“We’ll talk about it with the UFT and see if there’s some misinterpretation as far as our definition of what they mean by sunset and what we’re saying,” he said.

The union wants the plan to “sunset” after one or two years to allow officials to reexamine how accurately new evaluations are able to measure student growth in classes without state tests. City officials have said that no expiration date can be on the table because a sunset could slow down their ability to remove the lowest-rated teachers.

In the 12 days since a deal fell apart, State Education Commissioner John King and Gov. Andrew Cuomo have sided with the union on the sunset issue. They have repeatedly pointed out that most districts in the state agreed to one- or two-year deals.

But the city is balking on a shortened deal in part because officials say they don’t know if an expired plan would wipe out the expedited appeals process that was negotiated separately with the union last year. Under the new process, “ineffective” teachers who challenge their ratings have to present evidence for why the rating is wrong, a much steeper burden than what’s required in the current process, where the burden of proof is on the city.

Cuomo, King, and the UFT have all said that the city’s concerns are misguided. Today, Walcott said he’d be open to discussing that possibility in the negotiations, but then quickly added, “Sunset, to me, is not something we’re going to accept at all.”

Mulgrew said he was willing to forge ahead in the new talks but remained “skeptical.”

“I am very upset how these negotiations broke down,” he said. “I cannot believe the reasons that I’m hearing why the other side is saying they will not agree.”

In their testimonies, Mulgrew and Walcott stuck to their respective stories about what happened in the early morning hours of Jan. 17 that led to the deal’s collapse. The two accounts directly contradicted each other and lawmakers grew frustrated.

“Someone ain’t being totally forthright. And I’m not accusing either side but this is absurd,” said Sen. John DiFrancisco, a Republican from Syracuse. The local conflict is of statewide interest because lawmakers have to decide whether to go along with Cuomo’s proposal to tie school aid to teacher evaluations for a second year. DiFrancisco and other lawmakers also express an interested in absorbing some of the state fundingt that New York City forfeited.

Nolan said many parts of government were to blame for the city’s failure to submit an evaluation in on time. But she said Mulgrew has an opportunity to now fix it to prevent further financial penalties.

“This is a mutual failure from all sides, and I am including the governor, the legislature, the council, the local governments, and, yes, labor and management — the mayor and you,” Nolan said. “And I hope that somehow you’ll find it in your hearts to put pride aside to put righteous anger and principles aside and try to make a deal for the good of the children.”