Like other Braintree officials, Town Councilor Paul “Dan” Clifford was dismayed to learn that Blue Hills Regional Technical High School had $857,000 in extra cash. Now he hopes the other towns that fund Blue Hills will tighten up their oversight of the school’s budget in the years to come.

Braintree — along with Avon, Canton, Dedham, Holbrook, Milton, Norwood, Randolph, and Westwood — approves the Blue Hills budget annually before providing an appropriation to the school, which is located in Canton. The appropriation is based on a state formula that factors in the number of students sent by the town and the town’s wealth.

Currently, each town reviews the school’s budget separately before bringing it to its Town Meeting for a vote. If six of the nine towns approve, the budget is enacted as presented.

It’s a divide-and-conquer approach that isn’t working, said Clifford, who chairs the financial committee that reviews Braintree’s budgets. According to Clifford, concerns about the budget came to light too late in the process, meaning there was little Braintree could do to change a budget that had basically taken effect.

Problems initially arose when the Town Council’s auditor discovered that Blue Hills previously had $2.5 million in its “excess and deficiency,” or free cash, account. Much of that amount was left over after several capital projects were scuttled, Blue Hills staff said. The remainder had been built up and stored away over time.

However, according to a state mandate, regional schools can carry up to 5 percent of their budget in the excess and deficiency account.

With a budget of $17.9 million, Blue Hills had to cut the funds substantially and gave back $1.65 million to several of the communities in the way of lowered assessments for fiscal 2013, which begins next month. That left about $857,000 in the account.

Still, Braintree councilors were uncomfortable with such a large sum being left in the account, especially with several of the school’s biggest unions currently going through contract negotiations.

As a compromise, Braintree suggested that Blue Hills give back another $450,000 to area towns through reduced assessments in fiscal 2013, proportionate to the towns’ contributions to the school.

Blue Hills Superintendent James Quaglia vehemently objected to that logic.

According to Quaglia, the remaining funds are to be used to reduce the towns’ assessments for fiscal 2014; otherwise, the towns would see a sharp increase in required appropriations.

“To produce a budget that is palatable to the towns, to create assessments that are reasonable, you have to trend your reserves over time,” Quaglia said in a phone interview. “If you don’t, and you’re not going to be reducing assessments with [excess and deficiency], then everyone’s assessment will uniformly increase, and we won’t pass a budget.”

Despite lengthy conversations with Quaglia in two meetings, Braintree officials were not swayed, and the town rejected the proposed budget at Town Meeting on May 29.

In mid-May Clifford had sent representatives of the other eight towns an e-mail outlining his concerns, but by that time, many communities had already approved the budgets.

In Avon, although officials sympathized with Braintree’s concern, a nearly $100,000 decrease in the fiscal 2013 assessment placated the town enough not to look too deeply into the remaining excess and deficiency money at the time of budget discussions, said Avon Town Administrator Michael McCue.

Canton, meanwhile, had received a 12 percent decrease in the appropriation and was happy with the budget, said finance director James Murgia.

Although Murgia said officials understood Braintree’s fears, the budget was approved prior to the complaint being raised.

Westwood officials said their town’s annual appropriation is so small that the Blue Hills budget isn’t thoroughly vetted, and was easily approved.

In Milton, the budget had also already been approved without question. “The proposal Dan mentioned to me was taking $450,000 and reducing the overall costs. It’s a good idea, but I said to him Town Meeting had already approved the budget,” said Town Administrator Kevin Mearn.

In Holbrook, town officials sided more with Blue Hills, saying they understood the concerns prior to approving the latest budget and didn’t see much wrong with amortizing budget deficiencies over time.

“The bottom line is [our finance committee] was aware of [the E&D account] when they voted on the budget,’’ said Holbrook Town Administrator William Phelan. “Their understanding is they would use a significant amount of that reserve for their 2013 budget, creating a structural deficit in their budget moving forward in future years. Although it’s a high reserve, it’s something they will be eating away at.”

Although Dedham rejected the proposed budget for other reasons, officials there said it wasn’t unreasonable for the school to keep 5 percent in reserve.

Norwood was also days away from approving its budget and couldn’t do much to change the appropriation.

Nonetheless, the revelation of what’s occurring in the fund has sparked curiosity, and officials said their eyes have been opened for next year.

“They were upset in Braintree,’’ said Judith Langone, chairwoman of the Norwood Finance Committee. “I was quite a bit upset, and at one point a Norwood School Committee person said, ‘Think about it like free cash, or a slush fund. You have no oversight and [they] can spend it on anything.’ . . . That disturbed me. But I can’t comment one way or another, right or wrong. I know it is an issue. It will be on our radar screen next year, and Blue Hills is aware that there are people looking at this much more closely.”

Randolph officials, who haven’t yet voted on the budget, could not be reached for comment.

Although Blue Hills’ budget has already been passed by the required number of communities for the coming year, officials in every community spoken to agreed that, moving forward, the towns should come together to review the budget as a group.

“I feel bad for Blue Hills,’’ said David Martin, chairman of the finance committee for Dedham. “They have to go to each one of the towns, a presentation to finance [committee], to Town Meeting. It’s an ordeal for them. If they could do it at one time, it would save everybody time and effort.”

For Clifford, the Braintree councilor, especially after this year, changing the way the system works is the difference in acting on something concerning in the budget and letting it fall through the cracks.

“I believe from a business practice, it’s the best way to go,” he said. “That we do our due diligence in advance of town meetings, so everybody has an equal chance and understands where concerns are in the budget and act as one rather than nine.”