BELFAST, Maine — Voters from the nine towns of Regional School Union 20 resoundingly rejected Tuesday the $33.5 million budget proposed for the next year — the second time in two months that residents have rejected the proposed budget.

Altogether, 965 people in the communities of Belfast, Belmont, Morrill, Northport, Searsmont, Searsport, Stockton Springs and Swanville voted against the budget, with 417 people in favor.

The vote marked the latest volley in what has felt like a summer-long tennis match between two vocal — and very different — types of voters: those who favor cutting property taxes for schools and those who wish to maintain current curriculum and extracurricular activities. The most recent version of the budget contained cuts for art teachers, among other positions.

“It’s interesting how some people think that art is the lowest part of a totem pole and should be looked at like recess or something, when it’s one of the most important things that ties all the core subjects together,” Russell Kahn of Belfast, who teaches art in a nearby school district, said Wednesday. “If they want to save money at this point, why not look at the possibility of pay to play [sports], instead of always going after music, art and physical education.”

John McDonald, the assistant superintendent of RSU 20, said that in his seven-year tenure at his position, he’s never known a proposed budget to fail twice. Part of the issue may be that a small percentage of voters — who generally have a strong interest — come to the final budget meetings and fine-tune that document. But they likely do not represent the 10,000 potential voters in the county, he said.

“We certainly have folks who’d like to add positions back into the budget, such as the art positions. And we have folks who would like to see their taxes go down,” McDonald said Wednesday. “It’s really tough. We go back and forth. The budget’s raised, the voters vote it down. The budget’s lowered, the voters vote it down. And that’s the law on the books right now. There’s no alternative to that process.”

The process is beginning to wear on people, including Superintendent Brian Carpenter, who said that the voters’ latest decision has left him with a lot of questions.

“The bottom line is, what do people want?” he asked. “There will be different cuts, probably. We’re brainstorming ideas, including charging students to park their cars at school. This last vote didn’t tell me a thing.”

Jim Rier of the Maine Department of Education said that RSU 20 and the Auburn School Department are the only two districts out of the state’s 220 that have had budgets fail twice this summer. He said that four or five districts statewide still have no set school budget.

Without a validated document, RSU 20 will use the $33.5 million approved at the last budget meeting as its operating budget until voters approve a new one.

“Municipalities are going to get very concerned,” Rier said. “They will struggle also, until they have a finally approved budget. It’s very difficult for them to send out tax bills.”

Richard Couch, the town manager of Stockton Springs, said that while he will collect the taxes according to the bill the school district sends to his town, the uncertainty and the cost of the election process are worrisome.

“Every school election costs $15,000. That’s money that’s not going to buy school supplies. It’s not going to buy a school lunch program or pay for buses,” he said. “That’s money that’s going to pay to administer an election at least one more time. That’s troubling to me.”

But Chris Bitely, a Belfast parent and property taxpayer, said that he has some larger worries.

“I’m concerned that the people who make the budget are not able to properly assess how to make a budget that the public will pass,” he said. “It feels like there is a divisiveness surrounding the tax issues that may be mirroring the larger national divide we have over taxes. Most reasonable people want what’s best for the students — but there are people drawing that line in different places.”

All this back-and-forth is particularly hard for those who are waiting for a final budget in order to move on with their lives — including Rob Brown of Northport. His wife, Nancy Brown, teaches art at Searsport District Elementary School and her job is in jeopardy. He said he believes that the RSU 20 board of directors and Superintendent Brian Carpenter could do a much better job.

“I feel like the onus is on them to have a decent, quality educational system while keeping property taxes in line. Those things are not mutually exclusive,” he said. “They need to start from scratch. They need to think about what kind of infrastructure is needed to adequately educate students in this district.”