Months after a deal to let a handful of city schools receive federal funding, requirements continue to keep millions of Race to the Top dollars off-limits to all but 2 percent of city schools.

When New York State won $700 million in the federal Race to the Top competition last year, it put some funds to use on statewide initiatives. But nearly $350 million went into smaller funds with specific aims: to build new curriculum models or train teachers, for example. Now, the state has started opening those pools up to districts — but it has set an eligibility requirement that the city can’t meet.

The state requires that districts commit to putting new teacher evaluations in place by next year — with union support. That requirement can be found in several of the Requests for Proposals for Race to the Top-related initiatives that the state has begun releasing.

In one application for funding that it submitted last week, the city could not show it had the union’s support for the new teacher evaluation system in most of its schools, in the form of a required Memorandum of Understanding, so it only applied for money for the 30 schools that do.

Those 30 schools are among 33 included in a partial teacher evaluation deal hashed out this summer, when the union and city saw that federal school improvement grants were at stake. At the time, UFT President Michael Mulgrew said he wanted to see the outcome of the pilot before expanding the evaluations to more schools. And as the year has worn on, slow-moving negotiations about the new evaluations have seemed headed for an impasse.

This week, charging that some principals are using the new evaluations even though the old system is still in place, the UFT is threatening to participate in talks only to the bare minimum required by law.

The decaying union-city relations could help explain why, when it submitted a bid last week for teacher training funds, the Department of Education asked for its share of Race to the Top funds to go only to schools included in the limited evaluation deal.

According to Barbara Morgan, a DOE spokeswoman, the city said it was asking for $10 million to pay for teacher training at the 30 schools but also listed 100 schools that could use the money if they also undergo federally-funded “transformation” or “restart” processes.

Michael Mendel, the UFT secretary who said he would typically review documents such as the MOU, said the department did not present an MOU about the induction program to him or, to his knowledge, to anyone else at the union.

He also said that the deal struck this summer applies only to the 33 schools that are undergoing “restart” and “transformation” right now, even if the city later selects more schools to undergo those programs.

It’s unclear whether the state would approve the city’s funding bids without the memorandums in place. If the city’s application is turned down, the funds would be dispersed among other districts, according to Race to the Top rules.

This standstill could cause problems for future RFPs. The next grant, which opened up to applications last week and would fund principal training programs, also requires a union signature.