Gideon L. Nadeau Sr., chairman of the selectmen, said those expenses include bond payments and payroll.

According to the application, which selectmen said was sent Thursday, Troy isn’t able to finance its operations because its 2013 tax rate hadn’t been set, and it can’t borrow any more money to pay its bills.

The N.H. Department of Revenue Administration isn’t able to set the town’s tax rate because of a petition the selectmen filed with the N.H. Department of Education on Nov. 1, the application stated. The petition challenges the legality of a petition warrant article Monadnock Regional School District voters approved at the annual meeting in March.

Troy selectmen say the article wasn’t recommended by the Monadnock School Board, and that violates state law.

The article, which went into effect July 1, changes the formula used to calculate the amount each town pays Monadnock annually, to be based on 75 percent student enrollment and 25 percent town property valuation.

Before July 1, the formula was based on 50 percent student enrollment and 50 percent town property valuation.

Besides Troy, the school district covers Fitzwilliam, Gilsum, Richmond, Roxbury and Swanzey.

Marc Goldberg, communications director for Gov. Hassan’s Office, said Friday the state office has received Troy’s application for assistance. The issues outlined in the application are being reviewed by the N.H. Attorney General’s Office and other state agencies, he said.

One of those agencies is the Department of Education, which certified the vote on the formula change in July, saying it was “lawfully adopted.”

Goldberg didn’t say how long a review would take, and said additional information would be provided when available.

At the state Board of Education’s monthly meeting, which was held at Monadnock Regional Middle/High School in Swanzey Center Thursday, board members voted to request a legal opinion from the state Attorney General’s Office before responding to Troy’s petition about overruling the March vote.

During the public comment portion of the Board of Education meeting, Troy Selectman William T. Matson stressed to board members the importance that they act quickly on the matter.

He said in a phone interview Thursday that in a situation where the town didn’t have enough revenue to cover its bills, it would borrow money on a tax anticipation note. Usually that would happen at the beginning of the year, as the first tax bills aren’t sent out until the spring, he said.

The tax bills issued in the fall would be used to pay off that tax anticipation note before the end of the year, he said.

However, this year, the fall bills had yet to be issued because the tax rate wasn’t set, Nadeau said. As a result, the town isn’t able to pay off the roughly $500,000 tax anticipation note, he said.

Aside from the tax rate situation, Troy selectmen are concerned about the change in the Monadnock Regional School District funding formula to be based on 75 percent student enrollment and 25 percent town property valuation.

Despite Troy’s petition, the N.H. Department of Education gave the state Department or Revenue Administration the information it needed to begin setting tax rates for Monadnock’s member towns earlier this week based on the 75/25 split.

On Friday, the Department of Revenue Administration set Troy’s 2013 tax rate at $36.26 per $1,000 property valuation, which is an increase of about $10, or 26 percent, from the 2012 tax rate of $26.77. Of the $36.26 per $1,000 property valuation, $20.32 is the local education tax based on the new school funding formula. Troy’s local education tax in 2012 was $11.51 per $1,000 property valuation.

The selectmen have since sent a letter to the N.H. Department or Revenue Administration protesting the total tax rate.

Troy and Swanzey were the only Mondanock towns to vote against the formula change at the school district’s annual meeting. Troy residents overwhelmingly voted down the warrant article 213-64, even after one of the town’s representatives on the Monadnock School Board, Richard H. Thackston 3rd, spoke in favor of it. He told The Sentinel in March that it was a good compromise and seemed “inherently fair.”

Under the 75/25 split, Troy’s apportionment for operating and capital expenses to Monadnock for 2013-14 is about $4.6 million before state aid. The amount is an increase of $635,821 from the 2012-13 apportionment of approximately $3.96 million.

With state aid, the town’s apportionment for 2013-14 is slated to be about $2.18 million.

If the school funding formula was still based on 50 percent student enrollment and 50 percent town property valuation, Troy would owe Monadnock approximately $4.19 million for the 2013-14 school year. After state aid, Troy’s payment would be about $1.78 million.

Since 2009, Troy’s apportionment after state aid to Monadnock has accounted for 35 to 45 percent of the town’s total annual expenditures.

Troy’s apportionment after state aid for 2013-14 is about 52 percent of the town’s 2012 expenditures.

The change in the school funding formula isn’t the only reason Troy’s school costs have increased. Monadnock officials have said decreases in state aid and the July 1 withdraw of Sullivan from the school district have also contributed the apportionment changes in Troy and the district’s five other towns.

Besides Troy, Gilsum and Swanzey saw their payments increase for 2013-14, while Fitzwilliam, Richmond and Roxbury saw their payments decreased.

Making it even more challenging for Troy to handle the change in apportionment is that voters approved a town budget in March that didn’t account for a change in the school funding formula, town officials said.