Dolphins don't breathe automatically/ involuntry. - they breathe when they tell themselves to breathe.
More Info: When dolphins sleep, they lie on their side with their blowhole above the water surface. They sleep with only half of their brain at time, and they take turns sleeping with different sides of its brain. The other half stays awake so the dolphin remembers to breathe. This also means that dolphins cannot receive anesthetics because they will stop breathing.