Often public pools have diving boards and they are fully legal. Local laws determine whether the body boards can be used in the public swimming pool. Check for signs.
Pool boards are indeed legal in public pools, provided they meet certain safety standards. With proper supervision, height and depth requirements, pool boards can be quiet safe.
I assume that you are referring to a diving board here. This is perfectly legal, I imagine that the pool owner has to pay for it in their insurance premium.