I was paddled (twice I think) in the 8th grade - California public school in the 1950s. As I remember, every teacher had a paddle but some were more apt to use it than others; shop teachers & gym coaches were the most likely. I got mine from a shop teacher for fighting on the playground.

My homeroom teacher was also quick to paddle. The culprit was called up to the front of the room and the class was instructed to put their heads on their desks with their eyes closed. We would then hear 2 or 3 swats administered. He also would take a ruler to the palm of your hand on occasions; I got that a couple times as well.

I don't know if there was a rule in place, but in practice only boys got swats in my school.