The district currently has one SRO who covers both the Pequenakonck Elementary School and North Salem Middle/High School.
The board shot down a proposal for a second SRO earlier this month.
Families testified at a school board meeting Wednesday to try to get the board to reconsider their decision.
Parent Eric Buzzetto told the school board to think about what the district would do in the case of a mass shooting.
"Our schools are three-quarters of a mile apart, and to have one person in between two is very hard for that person,” he said.
Board President Andrew Brown, who is also a longtime police officer, said mental health professionals and guidance counselors are just as important to creating a positive school climate and preventing violence.
"The reality is SROs do very little to prevent shootings,” he said. "Kids overheard something in the mall, they call the school. Someone says something to a friend, they call the school. The state police, North Salem police or Westchester County police respond, and they've been investigating these incidents over the years."
The school board said it would take close to $100,000 to fully fund another SRO position.
Brown said it's very unlikely that the board is going to change their mind, but they'll seriously consider another SRO position in next year's budget.