Superintendent Jan Furman alerted parents that the district received a tip that a potential shooting may occur at the school during the week of November 8.
A heavy police presence will remain at the school through Friday, Furman said.
Students and staff must pass through metal detectors to enter the building for the rest of the week.
Students are also not allowed to leave the building for lunch, free periods or for any reason.
A canine sweep of Old Tappan and Demarest campuses was done to ensure no weapons in either building.
At Old Tappan, staff and students have been directed to report any unusual or suspicious activity to the Building Principal or Assistant Principals.
"In consult with law enforcement officials we urge all staff and students to maintain their regular school schedules this week as there is no credible evidence to support the tip at this time," Furhman said.
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