Given a second opportunity to vote on their school budget, residents of the Clarence School District voted overwhemingly to approve a budget, 3,541 to 1,817.

Voters approved the district’s second-chance budget by roughly 66 percent to 34 percent.

The approved budget in Clarence brings the tax rate under the state’s cap. The passage means the district will cut nearly 30 positions from its original budget, which was defeated last month, but avoid a “disaster” situation with even more staff and teacher cuts.

However, Wilson School District again turned thumbs down today.

But budgets were approved in the Lewiston-Porter, Niagara Wheatfield and Bemus Point districts.

The Wilson budget was defeated 903 to 604.

In Lewiston-Porter, the budget was approved, 1,663 to 993; in Niagara Wheatfield, the margin was 2,402 to 1,795; and in Bemus Point, 601 to 440.

Altogether, voters in six Western New York school districts went to the polls a second time in two months today, as districts offered budgets for a revote.

Statewide, 32 of 676 budgets were defeated in May. Voters considered new budgets in most districts, although some districts submitted the same budgets that were defeated last month.

Some budgets, like those in Clarence and Lewiston-Porter, would spend less than this year. The tax levy in those and in Alden, Niagara Wheatfield, Wilson and Bemus Point would go up, although none of the levies is above the tax cap, and all needed a simple majority to pass.

The Clarence school vote got a lot of attention after last month’s resounding defeat of the original budget that called for a 9.8 percent tax increase.

Turnout for the Clarence school revote was steady throughout the day but not as high as when the first budget was defeated a month ago.

More than 5,300 voters had cast their ballots, the second-highest vote total in the history of the district.

The consequences of a second budget defeat can be dire to districts. Their school boards must adopt budgets that do not increase the tax levy from this year. That means cuts of several hundred thousand dollars to more than $1 million to others, such as Clarence.

Last year, there were 24 revotes, and only two districts in New York State operated on contingent budgets: Cheektowaga Sloan, and Oppenheim-Ephratah Central in Fulton and Herkimer counties.

“Crafting budgets this year was like walking a tightrope. Move too far in one direction and you cut too deeply into educational programs. Move too far in the other direction and you run the risk of exceeding your tax levy limit,” said Timothy G. Kremer, executive director of the New York State School Boards Association.