You could, but chilled water circulation is the more typical heat transfer medium in central, building-wide units. Water can carry a lot of heat, is cheap and readily available, non-polluting, non-toxic, easy to pump, easy to plumb, and liquid at temps convenient for heating and cooling.

The first apartment building I lived in in NY had this. The only downside was that if the board put off maintenance so long that one summer the cooling towers were busted, then they waited until may to start the project to replace them, then an early heat wave came, it could be darn uncomfortable for a week or two. (That did indeed happen, just like I told it.)