Efforts to rebuild the aging Martha’s Vineyard Regional High School are at a standstill again, with five towns willing to proceed but a sixth digging in its heels.

Reigniting a longstanding dispute over how high school costs are divided among Island towns, the Oak Bluffs select board declined Tuesday to sign a joint letter to the Massachusetts School Building Authority (MSBA) promising a “good faith effort to support a building project.”

The state has not removed the high school from its list of 58 contenders for the highly selective program, which admits fewer than 20 school construction projects a year and pays up to 38 per cent of the cost.

But a regional school district that cannot agree on its own cost-sharing formula is not a strong prospect for state support, MSBA executive director Jack McCarthy told the Gazette Thursday afternoon.

“Our statute only allows us to approve so many projects [and] it’s a dollar amount. We’re capped,” Mr. McCarthy said.

“We can’t keep up with all of the requests. That’s one of the reasons we take preparedness seriously,” he said.

Island school officials’ hopes for a 2022 acceptance had soared in recent weeks after a conference with town representatives and MSBA officials, held at Mr. McCarthy’s request to gauge local support.

“As part of our due diligence, we always try to find out, if we invited a district in, would they be ready to proceed?” Mr. McCarthy said.

“We took note that in 2019 [the district] tried to do a feasibility study . . . and we noted Oak Bluffs was the only town [against it],” he said.

“I specifically asked the question, ‘Tell me what’s different than [in] 2019?’ There was a representative from Oak Bluffs on the call [who] indicated in his opinion that things had changed,” Mr. McCarthy said.

“It doesn’t seem like that’s occurring,” he added.

Arguing that they do back the effort to build a new high school, Oak Bluffs select board members said Tuesday they would draft their own letter to the MSBA, calling for a conversation on the school formula.

“Unfortunately I can’t sign a letter that says I’m going to work in good faith when I know that [the] funding [formula] doesn’t work,” select board member Jason Balboni said.

Town leaders have maintained that the funding formula, which is based on enrollment, is unfair and disproportionately burdens Oak Bluffs taxpayers.

But Mr. McCarthy indicated that his agency, which is funded from a portion of the state sales tax, prefers not to be pulled into local disputes.

“We don’t like to see projects used as leverage,” he said. “The only consideration should be what’s the best thing for the kids and how does that make sense for the funding.”

Acceptance to the state building program is critical to a successful high school project, Island schools superintendent Dr. Matthew D’Andrea said Thursday.

“They bring the expertise, they bring resources [and] they bring the money,” he said.

“They know exactly how to do the process, and how to do it the most effective, efficient way possible, so you don’t run into problems down the road,” Mr. D’Andrea said. “To partner with them is very, very beneficial, apart from the money.”

The grant program provides about 37.9 per cent of construction costs up to $360 per square foot, MSBA director of operations Matt Donovan said.

The Tisbury School was accepted into the program in 2018, but was forced to drop out when a slender majority of voters defeated a ballot measure.

“We lost out on $14 million, and now we have a project that is going to cost the town $25 million more than it would have cost because of delays and, I would argue, not a clear understanding of what state support means,” said Amy Houghton, who chairs both the Tisbury and regional high school committees.

Without the prospect of state funding, Ms. Houghton said the high school district will need to begin piecemeal work at its own expense to keep the buildings functioning.

“There are multiple capital projects within the high school that can’t wait any longer,” she said. “Now the HVAC system has to be replaced . . . Projects we [thought] would be included in a comprehensive plan will now have to be done one by one.”

But Ms. Houghton also said she understands why Oak Bluffs wants to change the funding formula, which is spelled out in the regional district agreement, first written in 1954 and later amended several times. The funding formula for both the high school operating budget and also capital projects remains based almost entirely on town-by-town student enrollment.

As spelled out in the terms of the agreement, the high school committee or any member town can propose an amendment, but any amendment would need to be approved by all district towns.

Ms. Houghton said she believes more discussion is in order.

“I think that there’s a valid argument for saying, this is a community facility . . . and not just for those students who happen to be there on a given day,” Ms. Houghton said, adding that enrollments at some Island town schools have been fluctuating in recent years.

“The swing in enrollment is very real, and the impact in assessment to each town is very real,” she said.

Mr. McCarthy said the MSBA is also looking for change.

“This discussion on Martha’s Vineyard been going on for a long time,” he said. “They need to fix it.”

Aidan Pollard contributed reporting.