How do doctor's tell how long a body has been dead?

doctors will preform autopsy's to be able to evaluate how long a body has been dead and what the cause of death was

Explanation:

doctor's will do one of these tests Ancillary test or apnea test to Determine the time of death

"The person must have an apnea test. Then you can prove to yourself that the whole brain, including the brainstem, is gone. Just remember, when you take a patient off a ventilator, either for an apnea test or after a declaration of death, make sure that family members are out of sight, and forewarn the nurses. Many brain dead patients, once the ventilator is removed, exhibit the so-called Lazarus sign, where their arms spontaneously contract and their hands come up to their chest as though they’re grasping for the endotracheal tube. It’s creepy no matter how many times you’ve seen it."

Work cited:

How Doctors Determine the Moment of Death [Excerpt]

The definition of death is hazy but important for medical decisions, explains Harvard neurologist Allan Ropper in the new book Reaching Down the Rabbit Hole

By Allan Ropper and Brian David Burrell

i think its pulmonary not sure tho