WESTPORT — Police were dispatched to all town schools Monday “out of an abundance of caution” after “swatting” incidents — false threats — were reported at other school districts in Connecticut and New York, according to Supt. of Schools Thomas Scarice.

The police deployment, made in consultation with Police Chief Foti Koskinas, came after Scarce said “vague threats” were called in to schools in “multiple” districts, although none of the calls came directly to any Westport schools.

Multiple law-enforcement agencies “are investigating” the incidents, Scarice said.

But as a precaution, Scarice said he and Koskinas agreed that additional officers would be dispatched to Westport’s schools to supplement the recently established School Safety Unit.

The superintendent noted the swatting incidents Monday took place nearly a year after a similar false report — an active shooter — caused Staples High School to be locked down and nearby Bedford Middle School to be issued a shelter-in-place order.