Gov. Dannel P. Malloy may have signed what supporters are calling a sweeping education reform bill Tuesday, but its 185-pages don’t begin to touch upon how the state finances all of its public schools.

That thorny issue is expected to be dealt with by the legislature next year or a court in 2014, the year the education adequacy lawsuit is scheduled to go back to trial.

The Connecticut Coalition for Justice in Education Funding sued the state back in 2005 alleging that under the state’s Constitution, not only are students entitled to a public education but they also are entitled to one that works, one that assures them, at minimum, an adequate education. The state Supreme Court agreed in a 4-3 decision in 2010, which sent the case back to the trial court.

In an effort to convince the state of Connecticut to settle the lawsuit out of court, the Connecticut Coalition for Justice in Education Funding has upped the ante by acquiring the pro bono services of a prestigious New York law firm with deep pockets.

Earlier this week, the organization announced that Debevoise & Plimpton LLP will take over as chief legal counsel. Yale Law School’s Education Adequacy Project will continue its pro bono involvement with the case, but instead of being the lead law firm it continue in a supporting role.

And, after guiding the case to a Supreme Court victory, Yale doesn’t mind taking a back seat.

“We are delighted that Debevoise & Plimpton, one of the nation’s leading law firms, has agreed to join this vital lawsuit,” Yale Law School Dean Robert C. Post said. “The students of the law school’s Education Adequacy Project have litigated this case since it was filed in 2005, and we are grateful for the participation of Debevoise as the case moves into the trial stage.”

One of Debevoise & Plimpton’s most talented litigators, Helen Cantwell, a graduate of Harvard Law School, asked her firm for the case.

“I am extremely excited about this opportunity to lead such an important case,” Cantwell, a Greenwich native, said in a press release. “The CCJEF lawsuit will allow us to fight for the improved capacity of Connecticut’s public schools to ensure equal educational opportunity for all students, whether poor, minority, immigrant, handicapped, or gifted.”

The Attorney General’s Office, which is defending the state, welcomed the new firm.

“We welcome Debevoise & Plimpton to this important case and look forward to a constructive and cordial working relationship,” the office said in an email.

But Dianne Kaplan deVries, executive director of the Connecticut Coalition of Justice in Education Funding, called it a “huge new development” in the case.

“With the formidable resources and litigation expertise of Debevoise & Plimpton and the continuing invaluable work of the Yale Law School Education Adequacy Project students, CCJEF now has the Dream Team,” deVries said. “The timing is perfect. The state’s broken school finance system is widely acknowledged by state and local policymakers, yet it remains unfixed.”

In the meantime, the Education Cost Sharing Task Force created by Malloy, who was one of the first plaintiffs in the lawsuit when he was mayor of Stamford, is expected to make their recommendations on how to change the formula in October. The group was formed back in 2011.