What requirement does the Church use to determine if someone is dead?
Death is the separation of the soul from the body. We have no way of knowing exactly when that occurs, so we look for a combination of medical signs.
The Church itself does not come up with the requirement for death. The way these things generally develop is that medical science comes up with different requirement for death that are then checked by the Church and accepted or rejected.
The combination of signs that modern medicine uses to officially declare that someone has died has not been controversial and has long been welcomed by the Church. The most recent criterion that has been somewhat controversial that has been accepted by the Church is that “brain death” is an acceptable criterion for moral certainty that a person has died.