is there a specific thing that a doctor can tell that a person is dead or not.

I think doctor check pulses...well dotors have domain knowledge and they cant be wrong

Even when you're in a coma you have a pulse don't you? Weaker than if you was alive and active. Although considering if that was missed some how, you're usually hooked up to so many machines monitoring so many aspects. If the causes are unknown, or even if they are known I believe a post-mortem is the next step.