Stonington — One day after taxpayers narrowly rejected the proposed 2012-13 budget and its 0.42-mill tax rate increase, the Board of Finance agreed Wednesday to cut $300,000 from the school budget and make other reductions to bring the tax rate to a 0.26-mill increase.

“If we don’t take it down now, we’ll be right back here again,” board member Dudley Wheeler said, referring to the possibility of a second defeat if voters feel the board did not make a big enough cut.

The next referendum is tentatively scheduled for June 5. This means there will be no time for a third budget vote before the board has to set a tax rate by June 15.

On Tuesday, voters rejected the $57.1 million proposal, which called for the town’s largest tax rate increase in five years, by 1,157 votes to 1,125.

In addition to the $300,000 reduction to the proposed $1.3 million increase to the school budget, the finance board decided to fund the currently vacant director of planning position for only six months, saving $50,000.

It also cut $25,000 of the $75,000 allocated to begin repairs to Hewitt Road as well as $25,000 for a piece of highway department equipment.

In addition, the board decided to take an additional $100,000 from its undesignated fund balance to offset the tax rate. That means the town will now use $900,000 from its surplus next year.

Board Chairman Glenn Frishman pointed out that when the board begins work on the 2013-14 budget, it will already be facing a $900,000 revenue shortfall, which is equal to almost one-third of a mill.

The proposed $56.7 million budget now calls for a $1.4 million, or 2.6 percent, increase and a tax rate of 15.89 mills.

When the finance board finalized the now defeated budget two weeks ago, it restored $156,000 that it had originally cut from the proposed school budget after a large group of school supporters urged it to do so. The school board will now have to cut that amount as well as an additional $144,000.

j.wojtas@theday.com