I would generally not use 'carcass' to describe a human body - only a dead animal body. 'Cadaver' or 'corpse' would be more common for describing a dead human body. 'Dead body' is (for me) appropriate for referring to animals or humans.

I tend to think of "carcass" as being an animal's body that has been disturbed or damaged in some way, either through decay, by being partially eaten by predators, or by being carved up by a butcher. "carcass" would never be used in the literal sense to describe a human body.