AUGUSTA, Maine — Gov. Paul LePage vetoed a Republican-sponsored bill that drew unanimous support in the Legislature, and the Maine Senate on Wednesday fell one vote short of overriding it.

The measure addresses how school districts organized as alternative organizational structures pass their annual budgets. The veto, which LePage issued Monday, is the governor’s fifth of the legislative session.

The bill, LD 521, would allow an alternative organizational structure to change the way it approves its annual budgets through a vote at a special district meeting rather than through a referendum vote during a statewide election.

The measure is sponsored by Sen. David Burns, R-Whiting, and is co-sponsored by six other Republicans.

Alternative organizational structures are a type of school district allowed under Maine’s school district consolidation law under which the member towns share central administration but maintain their own municipal school boards and budgets. Alternative organizational structures can choose to pass their budgets, which address the costs of central administration, at an annual budget meeting attended by residents or by a school board vote.

“I cannot support this bill because it moves away from the ballot box and moves toward special meeting,” LePage wrote in his veto message. “It empowers the boards of alternative organizational structures (AOS) to call for special meetings to enhance the power of the board. That new power is the power of the purse, approving the budget for each AOS. If the taxpayers choose to give up that power, it should be done knowingly and openly.”

During a public hearing on the bill in March, Burns said the measure would help alternative organizational structures make their budget approval processes “less complicated and more efficient.” The state Department of Education opposed the bill.

Burns said the special meetings held to approve AOS budgets “are poorly attended by voters, and I am told that most people question the need for this meeting.”

In the Senate on Wednesday, Sen. Brian Langley, R-Ellsworth, said senators should sustain the veto and suggested Burns bring back similar, more clearly drafted legislation next year.

Senators voted 23-12 to override the veto, falling one vote short of the necessary two-thirds threshold.

Lawmakers have so far attempted to override each of LePage’s previous vetoes but have been unsuccessful. The House on Tuesday fell short of overriding LePage’s veto of a bill that would have allowed school boards to hire superintendents who live outside their communities, even if local ordinances require the superintendent reside within district boundaries.