A federal program that has drawn criticism in recent weeks for supplying surplus military gear to local police has also provided high-powered rifles, armored vehicles and other equipment to police at public schools, some of whom were unprepared for what they were getting.

In the wake of school shootings in Newtown, Conn., and elsewhere, some school security departments developed SWAT teams, added weapons and called on the federal government to help supply gear. But now, the program is facing renewed scrutiny from both outside...