For some reason I always remember this as “Tommy the Turtle”. Good thing youtube has a copy to set me straight.
This is from 1951, but these kind of films were still being shown in the late 1960s and early 70s in Delaware elementary schools. In the first couple of grades, they had us crouch under the desks with our hands behind our heads for A-bomb drills, but later they started having us go into the hallways and huddle against the walls. Pretty much the same as California earthquake drills, only with deadly fallout expected afterwards.