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District results show that the budget received 1,135 votes in favor to just 265 against.
Mester, who was first elected in 2007, won a fourth term with 880 votes. Messner, who was first elected in 2013 and is the current board president, won a second term with 928 votes.
Challenger Rhonda Kaufman, a local parent who with dental practice in Putnam Valley, received 649 votes.
Under the district's at-large system, the top two vote recipients are the winners of the two seats. The new terms, which are for three years, commence on July 1.
Total spending, which would be $118,225,288, will rise by just 0.27 percent. The tax levy, which is the total amount of property tax revenue for the budget, will be unchanged at $105,968,116.
Tax rates, which measure what taxpayers will owe per $1,000 of assessed property value, are projected to rise by 0.14 percent in New Castle and by 1.92 percent in Mount Pleasant. The differences in tax-rate changes are because the towns do not assessed their properties at the same levels of market value. As a result, an equation called the equalization rate is used to apportion the tax burden.
The tax levy is subject to a state-mandated cap on annual increases while tax rates are not. Even if the district is collecting the same amount of taxes as in the prior year, taxpayers' bills can still go up if the total assessed values of local properties decline from the previous year.
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