The Oak Bluffs select board threw a monkey wrench into the latest effort to jump start a feasibility study for a new high school Tuesday, declining to sign a joint letter to the Massachusetts School Building Authority (MSBA) stating that the town would work “with a good faith effort to support a building effort at the Martha’s Vineyard Regional High School.”

Select board members emphasized that they support the effort to build a new high school. But a longstanding dispute over the regional school district funding formula reared its head again, and the board declined to sign the Islandwide letter presented by the school district, deciding instead to draft an alternate letter to the MSBA.

“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 town taxpayers.

The MSBA, which can provide significant reimbursement for qualifying school building projects, has denied efforts by the high school to get on the eligibility list for the last six years — citing a lack of unity among the six Island towns.

The latest effort to get back on the eligibility list began this month, with high school leaders drafting the letter of support for the Island select boards to sign. School superintendent Dr. Matthew D’Andrea said he had been approached by the MSBA to encourage a new application — as long as the Island could demonstrate unity.

“They reached out to me and said, please would you set up a meeting with each of the six towns,” Mr. D’Andrea told the board Tuesday.

With a sudden deadline of Jan. 28 for submission, the letter is being circulated this week among Island select boards. West Tisbury has already signed the letter, while Edgartown agreed to sign it on Monday and Chilmark concurred at a meeting Tuesday. The Tisbury select board was due to take up the letter at a special meeting Wednesday.

But in Oak Bluffs on Tuesday, the momentum shifted.

MacGregor Anderson, the town principal assessor, gave a presentation showing a rough estimate of the average taxpayer in each town would be affected by the burden of a new high school. His model showed that Oak Bluffs and Tisbury would be more heavily affected than the other Island towns — with Aquinnah, Chilmark and Edgartown paying a smaller share of construction costs.

The high school building, which has not been updated since 1995, is in extremely poor condition. Early estimates show a new regional school will cost up to $100 million, although no feasibility study has been done yet. A formal study was proposed in 2019 but blocked by Oak Bluffs voters at the annual town meeting, led by school leaders who represent the town on the regional high school district committee. At the time school leaders called it a symbolic gesture of protest over the funding formula.

Efforts followed among the towns to reach some accord over the formula, but fell apart.

Select board chairman Brian Packish said Tuesday that without some kind of action on the formula, the town cannot join the letter to the MSBA. Other board members agreed.

“I’d like to sign the letter,” board member Emma Green-Beach said. “But the situation is unfortunate.”

The board agreed to draft an alternate letter, indicating the town is in favor of building a new high school, but requires a conversation regarding the school funding formula.

Assistant superintendent Richard Smith urged a regional approach on the effort to build a new school.

“I hope the narrative is this is an Island issue,” Mr. Smith said, “and as such is [handled] Islandwide.”

Despite their unwillingness to sign the letter, board members agreed that a new high school is imperative, and hope to continue working towards its construction.

“I personally think that we can get through this conversation,” Mr. Packish said.

Corrected from an earlier version which stated the funding formula is based on real estate valuations. The formula is based on enrollment.