Circulation occurs in three places... the perivisceral coelom, the water vascular system, and the hemal system There are hemal channels forming rings around the central part of the body around the mouth, and a third ring around the digestive system There are also radial hemal channels running down the rays next to the gonads. The hemal system seems mostly organized to distribute nutrients from the digestive tract.
The starfish has a water vascular system in which the exchange between oxygen and carbon dioxide occurs. The tube feet of the starfish act like gills. The Oxygen enters the water vascular system through the tube feet as the carbon dioxide exits the body.