You can have an erection after you die, especially after a hanging.

A sudden spinal cord stimulus can trigger an erection as a response. Also, a thoracic spinal cord injury releases the central nervous system's inhibition of an erection. The subsequent erection is an uncontrollable reflex action. Men who have suffered these injuries often have erections of varying hardness and duration. It has even been observed in men posthumously, after a hanging. It also can occur to animals.