At least two of New Orleans’ best-ranked public schools are getting ready to take their fight over state funding to the courts, escalating a conflict over how to dole out money for students with special needs.

Lusher Charter School and Lake Forest Charter Elementary School have both authorized litigation in case a vote Thursday at the state Board of Elementary and Secondary Education goes against them, which appears likely. The board of Ben Franklin High School is scheduled to discuss the issue at a special meeting Tuesday, and the board of Audubon Charter School is still weighing its options.

James Brown, an attorney for Lusher who also has been hired by Lake Forest to pursue legal action if necessary, said the schools are asking BESE to at least delay a vote. But he added that if the board moves ahead, a lawsuit “becomes something we really can’t avoid.”

A local task force made up of school leaders and others has already approved a new funding formula, and the heads of both school districts that operate in New Orleans are backing the approach, which will shift money to schools that enroll more students with disabilities. The state board’s vote would make it final.

The overarching question involved in the dispute is how to devise a fair method of divvying up state dollars in a city where nearly every school now operates as an independent charter school.

The number of students with special needs — and the severity of those needs — varies widely from school to school. And many advocates say that the extra dollars already allocated under the state’s existing formula don’t go far enough, creating an incentive for schools to push out or avoid enrolling disabled students.

That may not be a problem in a traditional school district, which can shift money from school to school as need be. But in New Orleans, each charter is technically a district unto itself and gets its funding directly, so there’s no central mechanism to redistribute funds.

The new formula up for a vote on Thursday would introduce separate tiers of funding based on the particular needs of a student, starting at an extra $1,499 and going as high as $22,486. There are also extra dollars for students who are over-aged or learning English for the first time.

The city’s selective magnet schools are against that shift for a number of reasons. They enroll fewer of the city’s special-needs students, and the new formula would include far fewer extra dollars for pupils designated as “gifted and talented,” who also require certain services by law.

The upshot would be a drop in funding for them, although state officials are pledging that no school will lose more than 2 percent of its allocation in a given year in order to cushion the blow.

The new funding scheme may also play into how schools in New Orleans are governed in the future.

The Orleans Parish School Board, which lost control of most city schools to the state-run Recovery School District after Hurricane Katrina, is trying to lure them back with a promise that they can hold onto the autonomy they enjoy now as independent charters. But those schools may be reluctant to return if they feel they won’t get enough funding for the most expensive students to educate.

The RSD moved to the tiered approach last year, while charters under the School Board — including the magnet schools — were left with the old formula, which gives schools a flat additional $3,236 for each student with special needs.

The local task force that has already voted to OK the new approach was created by the state Legislature last year to unify the city under one scheme.

The schools that have already decided to sue if BESE approves the new formula plan on pursuing a multipronged legal challenge. Brown, the attorney, said they will argue that BESE’s approval violates the state constitution, which calls on the board to establish one funding formula — known as the Minimum Foundation Program — that applies in every parish. And they will argue that singling out New Orleans also violates the U.S. Constitution’s guarantee of due process and equal protection under the law.

Brown said BESE does “not have the constitutional power to devise and impose a formula for 63 parishes and a different formula for Orleans Parish.”

District officials, on the other hand, point out that technically the MFP won’t be any different in New Orleans than elsewhere. The parish overall will get just as much funding per-pupil as it otherwise would, according to the same formula applied to other districts. The only difference is the way that money is then divvied up between schools, which can vary in other districts as well.

RSD spokeswoman Laura Hawkins provided a statement saying, “Superintendents do this in local parishes all across the state.”