HARTFORD (AP) — A judge's landmark ruling that declared Connecticut's system for funding its public schools unconstitutional is set to go before the state Supreme Court.

Justices are scheduled to hear arguments Thursday in the state's appeal of the ruling. The hearing comes as Democratic Gov. Dannel P. Malloy and legislators are mired in a budget impasse that includes debate over how the state should distribute education aid to cities and towns.

In September 2016, Superior Court Judge Thomas Moukawsher ordered state officials to develop plans for an overhaul of the state's public education system within six months, saying a huge gap in test scores between students in rich and poor towns shows parts of the system are unconstitutional.

Moukawsher ordered the state to submit proposed reforms to the court to revamp its formula for providing education aid to cities and towns, develop a statewide high school graduation standard such as a test, make eighth-graders show they have acquired the skills to move on to high school, and replace what he called a weak statewide system of teacher evaluation and compensation.

The judge also declared the state's program for special education spending "irrational," saying the process by which students get chosen for special education is "mostly arbitrary and depends not on rational criteria but on where children live and what pressures the system faces in their name."

"Beyond a reasonable doubt, Connecticut is defaulting on its constitutional duty to provide adequate public school opportunities because it has no rational, substantial and verifiable plan to distribute money for education aid and school construction," Moukawsher wrote in the decision.

The ruling came in a lawsuit filed in 2005 against the state by the Connecticut Coalition for Justice in Education Funding, a nonprofit group that includes cities, towns, local boards of education, parent groups and public school students. More than 50 parents and students were also named as plaintiffs.

The coalition alleges the state isn't providing adequate education funding to cities and towns and isn't meeting its constitutional obligation to provide all students with adequate educations. It says vast differences in test results, graduation rates and other factors between rich and poor towns show the funding system isn't fair.

"The future of K through 12 public education is at stake in this case," said James Finley Jr., the coalition's principal consultant for operations and government relations. "It's been a long road. We're happy we finally have our day before the Supreme Court."

The state attorney general's office, which is defending the state against the lawsuit, declined to comment.

Democratic Attorney General George Jepsen has said the legislative and executive branches of government are responsible for setting education policy, not a single judge.

"This decision would wrest educational policy from the representative branches of state government, limit public education for some students with special needs, create additional municipal mandates concerning graduation and other standards, and alter the basic terms of educators' employment — and entrust all of those matters to the discretion of a single, unelected judge," Jepsen said in a statement a week after the ruling.