Smithtown school district officials, faced with declining enrollment and rising costs, are considering closing Branch Brook Elementary School either by this fall or the 2017-18 school year.

Opponents said the proposed closure would scatter Branch Brook children among different schools and depress property values. It would be the second shuttering of a district school in recent years: Nesconset Elementary closed in 2012.

About 50 residents attended a work session Tuesday night at the Barton administrative building, 26 New York Ave. in Smithtown, where the plans were discussed.

Board members asked district officials about the upcoming budget and possible ways to save money. They also looked at the different student capacities in district schools.

Superintendent James J. Grossane noted unmandated programs such as full-day kindergarten and secondary electives could be cut. He also explained the impact declining enrollment has on the district.

Branch Brook, which serves 374 children in kindergarten through fifth grade, is the smallest of eight elementary schools in the 9,400-student district. Its enrollment is capped at 460, according to the district.

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The board is considering five options, including closing the school “no sooner than the 16-17 school year,” according to district documents. Of the five scenarios, Grossane is recommending two — both of which would close the school in fall 2017. Late Tuesday, the board said it plans to hold another work session, and added a sixth option to consider: closing Smithtown Elementary.

“This is a very difficult decision for the district to make,” Grossane said. “A building closure is strongly felt throughout the community, and is why the board has convened a series of citizens advisory councils on instruction and housing to examine the issue of declining enrollment within our district.”

School officials, in documents presented to the community, said K-12 enrollment has dropped every year since 2009 and is expected to drop to 7,300 by 2023. Closure of one elementary school would save about $725,000 each year, the district has said.

Of the two options Grossane is recommending, one would move 79 percent of Branch Brook students to Mount Pleasant Elementary and 21 percent to Smithtown Elementary. Twenty-three percent of students from Mount Pleasant would shift to Smithtown Elementary to balance the schools.

The second option would move 58 percent of Branch Brook students to Mount Pleasant, 21 percent to Smithtown Elementary, and 21 percent to Tackan Elementary School. In that case, 23 percent of Mount Pleasant students would go to Smithtown for balance.

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Five to 10 teaching positions would be lost if the school closes, officials said. Additional cuts would include positions for one principal, a nurse, and secretarial, custodial and other support staff.

The board also is looking into a complete redistricting. There would be no impact on the district’s three middle schools and two high schools.

Residents opposed to Branch Brook’s closure said they haven’t received full explanations of why Branch Brook was chosen, other than the argument it is the smallest school. They say Branch Brook has the highest number of children per classroom and is one of two elementary schools in the most densely populated area of Smithtown.

Parent Peter Troiano Jr. is among residents asking the district to reconvene a housing committee charged with picking an elementary school for closure. District officials, he said, did not take into account a number of factors, including the cost of utilities.

“We would be behind this if it was something that held weight,” he said, adding he thinks it does not.

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Supporters of the school launched a petition drive and have more than 500 signatures, according to an online website.

Closing an elementary school has been studied for at least a year, the district said in documents posted on its website. A committee of 25 members — representing every school, plus the Special Education PTA and the community at large — determined an elementary school’s closure was warranted to maintain a comprehensive, high-quality education and because of an expected decrease of more than 1,800 elementary-school-aged students by the 2016­17 school year, the district said.

Branch Brook’s size and location are among considerations for closing it, the documents said.