...When you where in Kindergarten , I was a Freshman in High School......any way, I don't recall seeing anything like that , but that doesn't mean there never was in the Topeka Public schools. At one point in time , Topeka was a target city due to Forbes Air Force Base. By the time I started school, 1970, all we had was fire drills and Tornado drills.
I would imagine that the signal(s) where sent via a dedicated phone line or much the same way a signal would have been sent to a siren during the Cold War era.
If there was threatening weather, I do know as a fact that there would be a phone call made from the NWS Topeka office to the Unified School Dist. office where they had the ability to call all the schools at once via telephone.