Two of the three up-Island towns that voted to reject their share of the regional high school budget last month have scheduled special town meetings to take a second vote on a budget that remains unchanged.

On Tuesday, the Chilmark select board set June 5 as the date for a special town meeting. West Tisbury had previously called a meeting for June 13. The Aquinnah select board was set to consider a June 6 date for a special town meeting, but their Tuesday board meeting was canceled.

The high school budget has become caught in the political crossfire over a plan rebuild the high school athletic fields using some artificial turf. The regional school committee is suing the Oak Bluffs planning board over its denial of the turf plan — and in an act of protest over legal spending on the case, at their annual town meetings this spring, the three up-Island towns voted to zero fund their share of the school budget.

That left the school committee with no approved budget less than three months before the start of a new fiscal year. State law requires regional school committees to come up with a revised budget if more than two-thirds of the school towns reject the budget.

After the town meeting votes, the school committee took steps to appease town meeting critics, voting to cap legal spending in the turf dispute and also to seek a settlement in the litigation. The details of the settlement talks remain in executive session.

At a meeting late last week the school committee voted to send the budget back to the three towns with no changes, noting that their pledge not to use the legal budget on the turf lawsuit in 2024 effectively addressed voters' concerns. In order for the budget to win approval, at least one of the three towns must approve its share of the spending.

Meanwhile, in addition to a second vote on their share of the budget, Chilmark voters will take up a pair of petitioned articles that seek to have the school swear off artificial turf.

On Tuesday Chilmark resident Sheila Muldaur presented the select board with two non-binding resolutions that call on the regional school committee to commit to all-grass playing fields at the high school, and not use any anonymous donations above $5,000 on legal fees, experts, design or permitting related to a plastic field.

“I feel like the school committee is not listening to the people,” Ms. Muldaur said.

The 10-article special town meeting warrant includes other items not related to the school issue, including a proposal to allow home delivery of marijuana products, funding to change the building inspector position from part time to full time and funding for a new ambulance.

Thomas Humphrey contributed reporting.