Loudoun County will pay $1.9 million to help cover a nearly $3 million overrun in the sheriff’s office’s fiscal 2013 budget, officials said Tuesday.

With the end of the fiscal year fast approaching, and the county sheriff’s office is on pace to exceed its budget by about $2.77 million, the Board of Supervisors was left with little choice but to recommend an additional allocation to help cover costs and avoid missed paychecks for sheriff’s office employees.

The budget overrun was announced by Supervisor Ralph Buona (R-Ashburn) at a March 7 budget work session. Buona, who heads the county finance, government services and operations committee, said he was equally troubled by the overspending and the fact that county leaders had not been told about it sooner.

“This overrun has not come to my committee. Nobody has come to the finance committee . . . and said, ‘We’re overspending.’ Nobody has said we had extraordinary circumstances, we needed additional appropriation . . . none of that has happened,” Buona said. “I’m learning that, with just over a quarter to go . . . in the fiscal year, you are significantly over budget. That’s troublesome.”

Sheriff Mike Chapman, who was at the March 7 work session, did not have an opportunity to reply to the development. The supervisors said he should expect to respond at a county finance committee meeting Tuesday.

Buona told Chapman to expect “hard questions” about the budget situation.

“When did you first learn about it? What have you done since you learned about it?” Buona asked Chapman at the work session.

At the committee meeting, Chapman offered a presentation to supervisors to address those questions and explain the overrun.

The biggest expenditure, according to the presentation, was overtime pay: Although the sheriff’s office budgets $2.6 million in overtime pay, most of the money goes to holiday pay and the cost of double-time pay for deputies who work when the government is closed. The remaining balance of a little more than $1 million is not enough to meet the department’s staffing needs, Chapman said.

The overtime costs were heightened this year by unusual circumstances, Chapman said. With Loudoun as a focal point in the national election, deputies were needed to staff several high-profile political campaign events. There were also additional staffing demands in the wake of severe weather, such as the derecho storm and Hurricane Sandy, Chapman said.

At the committee meeting, Chapman also emphasized one particular problem that he said was largely responsible for the sheriff’s office’s financial challenges: mandated vacancy savings.

The sheriff’s office is required to maintain 21 vacant positions, Chapman said, resulting in financial and operations failures and excessive overtime pay.

The 21 mandated vacant positions do not include the naturally occurring position vacancies, he said.

“This is where we have our most heartburn. . . . We’re down 30 positions that we have to then fill in some regard in order to provide some minimal level of service,” Chapman told the committee. “That’s really where it starts costing us quite a bit.”

The forced vacancies leave the agency in a bind, because other deputies must be paid to fill the empty posts, Chapman said. “We don’t have the option of just not having it filled. . . . We’re emergency service providers,” he said.

The committee members acknowledged that the issue of mandated vacancy savings needs to be addressed and said they would review the matter. Ben Mays, Loudoun’s chief financial officer, said it would cost the county about $5 million to eliminate vacancy savings across all county departments.

Supervisors Chairman Scott K. York (R-At Large) said it might be necessary for the county to absorb that cost.

“This is something we’ve got to take up very quickly, because quite frankly it doesn’t make any sense to tell somebody that they’ve got [full-time employee positions] but no, you can’t use them,” York said. “We may at one time have to take a one-time hit so that public safety can actually get the power on the streets, and in the long term, it’ll be savings if we don’t have to do overtime.”

During his presentation, Chapman also highlighted other cost-cutting measures that the sheriff’s office has taken, and said his staff had identified about $800,000 in operations and maintenance savings that could be applied to the fiscal 2013 overrun.

But supervisors were still concerned that the budget problems had not been brought to their attention sooner. Mays said the county finance staff frequently works to resolve budget issues directly with the department in question, and most matters generally need not rise to the board level. It is very rare for a department to exceed its budget by such a large sum, Mays said — and in this case, it wasn’t possible for the issue to be “worked out” between the finance staff and the sheriff’s office.

Supervisor Matt Letourneau (R-Dulles) asked why it wasn’t possible for the issue to be resolved.

“I don’t think I can answer that,” Mays said.

After the discussion, the committee members voted to recommend that the full Board of Supervisors allocate an additional $1.9 million to the sheriff’s office to cover the remaining cost of the budget overrun.