With the state Education Department directing school districts to share services, officials in the East Hampton and Springs systems recently reached an agreement that local administrators said kept Springs’ proposed 2016-17 budget from piercing the district’s tax-cap limit.

The arrangement, East Hampton Superintendent Richard Burns said, “is a prime example of what can be accomplished when schools combine resources.”

It came during a budget season marked by the lowest-yet baseline tax cap statewide, and as nine Long Island school districts are asking voters to approve spending plans that pierce their respective district’s tax caps. Six of those nine are small East End systems — Amagansett, Bridgehampton, East Quogue, Greenport, Shelter Island and Tuckahoe.

Voters on Long Island and across the state go to the polls Tuesday to decide district budgets, school board races and propositions on such matters as expenditures from reserve funds.

The tiny Springs district — with about 740 students in kindergarten through eighth grade, all housed in one building — was about $21,500 short when calculating its budget for next year, Superintendent John Finello said last week.

Plugging that gap by increasing the proposed budget and raising the local tax levy would have pushed the spending plan over the district’s 2016-17 tax cap of 0.13 percent, meaning it would pass only with approval by a 60 percent “supermajority.” A proposed budget that falls within a district’s cap requires a simple majority vote for approval.

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Looking to plug the shortfall, Springs entered into an agreement with the East Hampton school district that allows Springs’ seventh- and eighth-graders to participate on East Hampton’s athletic teams, including football, field hockey, cross country, wrestling, boys and girls lacrosse, and boys and girls track and field.

That savings pushed the Springs budget under its tax cap, officials said.

The $27,630,067 budget that voters will consider Tuesday represents a 0.97 percent increase over the current year’s. If approved, the tax levy would increase 0.13 percent — equal to the tax-cap limit.

The cooperative relationship had its beginnings earlier this school year, when Springs provided transportation to East Hampton students at no cost to the district. Springs students attend East Hampton High School on a tuition basis.

Finello said the two districts are examining yet more ways to pool resources, such as sharing a repair facility.

“It is something we should all be looking at,” he said.

Burns said he, too, is looking for more shared opportunities and has been in discussions with other East End districts, such as Montauk.

On the North Fork, the Greenport and Southold districts have shared a superintendent — David Gamberg — for the past two years and just extended the schools chief’s contract for another three years. The systems also share other administrative positions. Under the arrangement, Gamberg said each district has seen a $400,000 savings for the two-year period that began with the 2014-15 school year and will end in June.

Still, because of constraints under prior tax caps, the Greenport district had to eliminate a number of instructional positions. It is seeking to restore those this year with a proposed 2016-17 budget that asks voters to override the system’s 0.77 percent state cap.

“The point is we are doing everything we can to be cost-effective,” Gamberg said. “I am always on the lookout for other ways we can save.”