SHIRLEY — Having concluded after Annual Town Meeting two weeks ago that it was time to ask for a Proposition 2 1/2 tax override, selectmen last week agreed to appoint a seven-person committee to assist in the process.

On Monday, they followed through, establishing the Budget Coordinating Committee.

The committee won’t be asked to look into whether there should be an override election, but when such an event should take place and how much should be raised in an override.

Outgoing Chairman David Swain and newly elected Chairman Robert Prescott disagreed on those issues.

“I think it should be a week before (next year’s) Annual Town Meeting” and that two budgets should be presented” to residents at that time, Swain said.

That way, “if we don’t have enough money, they know it,” he said.

But Prescott felt that would be a mistake.

“We’re on a spending trajectory set by this Town Meeting,” he said. “So, yes, we need to have an override, but I really don’t want to go in with the same thing… we’ve been told what they want.”

Prescott’s reference was to the outcome of the recent Town Meeting, which rejected an administrative restructuring plan on which the balanced budget as presented was based. Several recommended line-item amounts in the omnibus budget reflected the plan.

Proposed by Town Administrator Patrice Garvin and backed by selectmen and the Finance Committee, the plan included reducing Town Hall hours and several town positions, along with their salaries.

But voters funded the original, requested amounts instead, restoring every position that was cut and for the most part tapping the stabilization fund to make up the difference.

Swain held out for his idea, however.

“If we approve a $600,000 override, (close to the currently projected deficit) but go into Town Meeting needing more” for the schools, it could cause another upset anyway, Swain said, citing unknown assessment hikes for Nashoba Tech and the Ayer Shirley Regional School District.

One thing the town does know, going in, said Selectman Kendra Dumont, is that with some department’s budgets level-funded for five years, line items would go up.

“I’m hoping the committee will look at that,” she said.

“I’d like to hear a lot of opinions,” said Garvin, who will serve in an advisory capacity on the override committee, which will meet weekly for the next three months — or more, if necessary — to produce a report and recommendations.

Also on the list of appointees are Town Clerk Amy McDougall, Principal Assessor and Finance Committee member Rebecca Boucher, Finance Committee Chairman Stewart Cady and members Brian Sawyer, Bryan Dumont and Paul Przybyla representing the community and a representative from the regional school district.

Betsy Colburn Mirkovic, whose application came in after the others, was appointed as an alternate.

The selectmen’s succinct charge to the Budget Coordinating Committee includes researching and expanding on existing information such as budget projections and the history of past overrides to spotlight “what the town truly needs to operate.”

The expected product will be a “short report” in three months but the time frame can be expanded if necessary, the charge states, with recommendations aimed at “logical steps” and “informed decisions” in terms of the proposed override.

In other business, selectmen signed the warrant for the June 8 Special Town Meeting, for which there will be one article: Realigning the municipal budget based on the outcome of Town Meeting.

According to Garvin, there will be four separate motions on the single article.

Two of the motions will address the two regional school-district assessments, which were rejected but are expected to bounce back with no changes.

A third motion under the “general government” category calls for a salary and cost-of-living increase for the town administrator.

The fourth motion will determine “final funding” sources for items Town Meeting funded via “raise and appropriate from available funds.”

The Super Town Meeting on Devens zoning issues that selectmen previously agreed to convene on the same night is still up in the air, as the other two towns — Ayer and Harvard — have not yet signed their Super Town Meeting warrants.

But the board voted to sign the second warrant anyway, “just in case.”

“All the towns accepted that date seven or eight weeks ago,” Swain said.