Do I have to post "No Trespassing " sign on property?

While the risk of liability to a trespasser is probably small, the school could conceivably be liable under certain circumstances, even if the person who was injured was a trespasser.  No trespassing signs would reduce the risk, but not eliminate it.  For example, if the school maintained a powerful, live electric wire, like a third rail, inches from the border of its property in an area where baseballs are often hit and retrieved by players on a nearby field, and neither placed explicit warnings or erected barriers to prevent people from touching the live wire, it would probably be liable to someone injured by that line when retrieving a ball, no trespassing signs or no.  The key is that the school has to act reasonably in light of the risks on its property.