Do starfish sleep? And if they do, where do starfish sleep? The easiest answer for this is no. They do not sleep. The long answer depends on the species of starfish you are looking at.
There are different body types of starfish, each with a unique behavioral mechanism and life history. Take the class Asteroidea, where there are more than 1800 known species, and Ophiuroidea with more than 1600 species. You will come across big and small types of starfish. Some of these animals will hide under the sand all through their lives while others will hide under rocks. You can also come across others that often move quite freely in the open.
For those that hide under the rocks or sand all through their lives, you might be tempted to assume that they sleep under their hiding places. As far as sleeping is concerned, starfish are always moving all the time. More often they are just looking for food. Some of them are scavengers and others are active predators. There are also starfish that are fully herbivorous.
You will also find starfish that only come out under the cover of darkness in the evenings, and people assume that they sleep through the day. In reality, during the day they are basically waiting. So, to answer the question where do starfish sleep, the easiest answer would be where they live (under rocks or under the sand) but that is not necessarily the case, because as we have already seen, they barely ever sleep in the first place.
Most of these fish possess a decentralized CNS. Because of this reason, their bodies are generally covered with lots of sensory cells especially at the tip of their arms. It is through these cells that they detect changes in the lighting conditions, chemical concentration, touch and change in currents around them. Given that most of them are highly sensitive, they respond so fast and this is why they are constantly moving from one place to the other.
There are species of starfish that will hide under rocks and opportunistically wait for their prey. The moment they sense the presence of their prey (dead fish or fish poop), they scurry out of their hideout, grab their food and tug it back to their hiding place to feast. So, technically, assuming there is no stimuli in their environment to challenge them to move to a different place, the starfish will do everything in their hiding place.