Starfish are slow-moving sea animals. To tell if your aquarium starfish is alive or dead, try to feed it. If the starfish does not respond, you'll need to physically examine it. This process should be done with the utmost care.
I'm Not Dead Yet
Starfish are typically nocturnal creatures, moving at night to feed. They also are quite content to hang around an aquarium without moving, which no doubt can cause panic. Another possibility to an unresponsive starfish is that the water in the tank is too aerated: Starfish prefer still water to move around in, and usually will remain in one spot in a tank with rapid currents, to "weather out the storm."
Some Gentle Care
If, however, your starfish has not moved for several days, and the water in your tank is calm, try to coax it with some tasty morsels of food. Prawns, mussels and other shellfish placed next to a hungry sea star will be too good to resist, and he should move on top of the food to eat. Before trying this, refrain from feeding your starfish for a day or two, as he may be waiting until night to eat.
If food prompts no movement, it's time to examine your sea star. Wear gloves, and move slowly and gently. A stressed starfish is more inclined to shed legs as a defense mechanism.
Look at your starfish before touching him. White spots or discolorations are a sign of sickness. The body of the starfish should be firm-looking, and not limp. Carefully touch the starfish on its underside before picking him up. If he's healthy, his tube feet should retract.
If you've carefully examined and touched him, and still are not sure as to whether he is a alive or dead, try gently picking him up. It's very important not to bring him above the water and into the air if there's still a chance that he may be alive: This kind of environment change shocks the body of even a healthy starfish. The body of a living starfish should be rigid against your hand. If he feels mushy, and there is no response, it is most likely that your starfish has passed.
It Doesn't End There
Once you've confirmed the passing of your starfish, it's vital to remove him from the tank at once. A rotting fish can spread disease or infection to your other aquarium tenants, not to mention pollute the water. You will want to determine the cause of death, so as to make sure the other creatures in your tank are not at risk. A local veterinarian specializing in aquatic care may be able to help by examining the deceased starfish. Although it is sad when a beloved pet dies, sometimes their passing can help reveal information about the tank before other lives are lost.