FARMINGTON — A top state Board of Corrections official says the Maine jail system is facing a $2.5 million budget shortfall this year even though it’s already cut back as much as possible on expenses.

The comment from Ryan Thornell, the board’s executive director, came in response to a decision Tuesday by the Franklin County commissioners to reject a $50,000 increase in its assessment. Commissioners again refused to pay the $50,000 billed by the State Board of Corrections, arguing the state does not have any legal authority to increase the payments due from the county.

Thornell said the county’s reduced payment is the least of its problems in light of the $2.5 million shortfall, which stems from a series of revenue problems, including a projected $500,000 decline in payments by the federal government for federal boarder inmates.

“There’s more urgent and more significant financial implications systemwide,” he said. “It’s not on the backs of Franklin County.”

The counties have little choice but to engage in deficit spending to run the jails, Thornell said, and he’s not sure how much the corrections board is allowed to spend with a deficit.

“There’s not more money to squeeze out of them,” he said.

The Franklin County commissioners unanimously voted Tuesday to pay $315,288 rather than the $365,288 it had been billed by the State Board of Corrections for the cost of boarding Franklin County’s long-term inmates at the Somerset County Jail in East Madison. The Franklin County lock-up holds inmates for up to 72 hours.

The $315,288 the commissioners voted to pay is the second of two annual installments paid by Franklin County to the state. In August, the commissioners also refused to pay $50,000 on the bill.

The Board of Corrections noted in its invoice that it considers the county’s balance to include $50,000 unpaid from the August billing in addition to the $365,288 for the current payment.

At a commissioners’ meeting Tuesday, County Commissioner Fred Hardy said he doesn’t think the corrections board demonstrated any legal grounds for charging the county an additional $100,000 for the year.

“I still haven’t seen any real proof,” he said.

Hardy has been a critic of the unified jail system adopted several years ago that reduced the facilities which house long-term county inmates. Hardy has claimed that the system takes financial problems that exist elsewhere in the state and makes them Franklin County’s problem.

Thornell said the board has not taken up whether to take legal action if Franklin County does not pay the money.

The money is paid to a state fund that is distributed to the jails that accept the longer-term, so-called “boarder” inmates. The impact on jail operations stemming from Franklin County’s decision to hold back on $100,000 won’t be known until budget balances run down toward the end of the fiscal year.

Thornell said the most pressing problem facing the state jail system is the predicted funding deficit, which continues to grow and is projected to be $2.5 million short of the estimated $83 million needed to operate the jail system for the current fiscal year.

Thornell said the board is requesting additional funding in Gov. Paul LePage’s supplemental budget and also will directly request funds from the Legislature’s Appropriations Committee.

In an interview Tuesday, Thornell said the jail system has had to engage in deficit spending in the past, but he is not sure if the corrections board even has the authority to run a deficit of upwards of $2.5 million.

The contentious relationship between Franklin County officials and state jail officials dates to a 2008 statewide jail overhaul that reduced the Franklin County Detention Center from a fully operational jail to a 72-hour holding center that must pay to board out its inmates to the Somerset County Jail.

The overhaul unified all county jails under one system governed by the State Board of Corrections, capped the amount of money jails can raise in property taxes and promised to pay any needed money over the property tax caps. Under the system, Franklin County pays about $600,000 a year in annual fees to the Somerset County Jail, where its inmates are held when they stay longer than three days.

Last May, the jail system was overhauled again in the hope of fixing years of funding shortages and weak State Board of Corrections authority. The corrections board members have previously voiced hope that the Legislature will have confidence in the new system and vote in the next biennial budget cycle to fully fund the jails for the first time.

Meantime, this fiscal year the board still is facing a steep shortfall, and Franklin County was among the jails seeing increased fees or reduced payments in an attempt to offset the shortfall.