The Catholic Church has long acknowledged the role of the medical professional in declaring death. It is the proper competency of medicine, not theology, to identify reliable signs that death has occurred.
The hardening of the body known as rigor mortis, for example, is a reliable medical indicator that death has occurred. When the heart permanently stops beating and the lungs permanently stop functioning (cessation of cardio-pulmonary function), medical professionals recognize these signs as another reliable way to assess that death has occurred.