Admittedly, a person who is sleeping does look a lot a person who is dead. After all, one of the behavioral hallmarks of sleeping is reduced muscle tone. This helps explain why people sleep in a sprawled out, horizontal position.
So, how can you tell that a person is sleeping and not dead? While both individuals are non-responsive (another behavioral indicator of sleep), this non-responsiveness is reversible for the sleeping individual. If you disturb that state of sleep, the individual will regain consciousness. Not so much for the dead guy.
Davis, H., Davis, P. A., Loomis, A. L., Harvey, E. N., & Hobart, G. (1937). Changes In Human Brain Potentials During The Onset Of Sleep. Science, 86(2237), 448-450. doi:10.1126/science.86.2237.448