The Fairfax County School Board approved a measure Thursday night that would allow the board to seek both fiscal autonomy and taxing authority from the state.

The 9 to 3 vote was part of the School Board’s 2014 legislative program, which asks the General Assembly to grant school boards the power to tax residents in order to generate revenue for classroom needs.

Fairfax schools face a $140 million deficit next year, and in almost any scenario the administration must make deep cuts to its $2.5 billion budget.

Every year, the board must ask for funding from the county Board of Supervisors. But in recent years, members of the School Board have said, the funding needs have not been met by the supervisors.

A solution for the dilemma emerged in Thursday’s meeting. School Board members have discussed in the past the possibility of local taxing authority. But the motion voted on by board members urged that “the General Assembly grant fiscal autonomy to elected local school boards.”

More than half of the Fairfax County budget is allocated to the schools. But with the ability to tax residents, the school administration would have more flexibility to address a shortfall like as the one they face this year.

“We want the fiscal autonomy — period,” said board member Patricia Reed (Providence), who proposed adding the motion into the legislative program to seek taxing authority.

“It’s an issue of accountability,” said board member Ted Velkoff (At Large), chair of the board’s budget committee. “If we’re the folks deciding how the money is going to be spent, I want to decide how it gets raised.”

Board member Elizabeth Schultz (Springfield) did not support the measure, which she said would hurt already burdened taxpayers.

“Fiscal autonomy for the School Board means that the School Board is going to come after your wallet,” Schultz said. “That’s the bottom line. . . . Watch out.”

But bringing tax authority to the Fairfax School Board could take time. To grant such authority, the legislature would have to propose amending the state’s constitution and then later place the measure before voters on a ballot referendum.