Connecticut students are among the highest-scoring performers in the nation. But New Haven may still have work to do.

According to scores released Wednesday by the state Department of Education, no state outperformed Connecticut’s eighth graders in the 2009 National Assessment of Educational Progress exam, a federal assessment in subjects including mathematics, reading and economics. And Connecticut’s results among fourth graders were second only to Massachusetts. Nevertheless, the test scores also indicate that class- and race-based disparities persist; Connecticut has the largest achievement gap in the nation, a significant problem in New Haven, city officials said. The state hopes to secure federal funding to improve the scores further, but it still remains unclear when and whether the funds will arrive.

The test results come just two days after the state Supreme Court ruled to require schools to meet its set standards, including preparing students to attend college and find jobs. State Education Commissioner Mark K. McQuillan said he was encouraged by the scores.

“We are pleased with our students’ overall performance,” McQuillan said in a statement Wednesday. “We know that progress is possible.”

But New Haven Board of Aldermen President Carl Goldfield said that despite the statewide increase in test scores, New Haven lags behind. The state’s average scores are high because of students from wealthy suburban towns like Greenwich, not poorer urban centers like New Haven, Goldfield said.

“Connecticut is not New Haven,” he said. “In the urban centers, you have large populations of poor people, kids who come from struggling, single-parent homes or homes without books.”

Michelle Wade, the director of communications for New Haven public schools, said the city’s current reform efforts aim to eliminate the achievement gap, reduce the dropout rate by 50 percent over the next five years and ensure that students have an opportunity to attend college.

At a time when New Haven is facing a multimillion-dollar budget deficit, the city is looking to the federal government for funds — including the “Race to the Top” grants announced in July 2009 by President Barack Obama and Secretary of Education Arne Duncan — to support education reform. But before New Haven receives any federal funds, it has to handle a number of bureaucratic hurdles, such as a report by the federal Department of Education last September, which charged that Connecticut improperly uses federal stimulus money.

After Connecticut was rejected from the first round of the Race to the Top grant, the federal government’s inter-scholastic $4 billion competition for school reform, Gov. M. Jodi Rell said in a statement earlier this month that the state is committed to applying during the second round.

“[This] is by no means the end of the process for Connecticut,” Rell said in the statement. “But it is obvious that we will need to do better — and we will.”

Nonetheless some school reform initiatives do not necessarily require an increase in funding, just a change in the way the school district does things, City Hall spokeswoman Jessica Mayorga wrote in an e-mail in January. She explained at the time that school reform does not have a “single dollar amount attached to it.”

Goldfield and Wade said they are optimistic about the future of education in New Haven.

“We’ve got a tough population here, but we’re not just laying back and saying nothing can be done,” Goldfield said. “What we are doing here dovetails perfectly with what the federal government is looking for.”

The second-round application for Race to the Top is due June 1.