Dead people get Goosebumps. But not in the same way that you and I do.
Goosebumps are small bumps on the skin, which form at the base of hairs on the skin. When we are cold or experience strong emotions such as fear or excitement, Goosebumps occur.
Goosebumps only appear where hair follicles are present. Beneath every hair follicle are tiny muscles that trigger a response for the hair to stand on edge. The tiny muscles essentially contract or flex, which causes the hair to stand up, and Goosebumps to appear.
It is something to do with trigger-response in evolution.
But why should the dead get Goosebumps?
When a person dies, one of the initial processes of decomposition is rigor mortis. When rigor mortis sets in the muscles contract and this causes the body to stiffen up. Just below the hair follicles lay tiny muscles, which also contract. When these muscles contract, the hairs stand on edge giving the appearance that the dead person has Goosebumps.
While Goosebumps on dead bodies can occur, it is far from a common occurrence. As they contract the skin around them takes on the appearance of goosebumps. Though the mechanism is the same as with the living but the trigger is not the same.