Final answer:
An incident that appears to be of a serious nature can be investigated under the direction of local law enforcement.
Step-by-step explanation:
An incident that appears to be of a serious nature can be investigated under the direction of local law enforcement (option b).
Local law enforcement agencies have the authority to investigate crimes and incidents that occur within their jurisdiction. They have the expertise and resources to handle serious matters and ensure that the appropriate actions are taken.
The facility director (option a) may have some role in addressing and reporting the incident, but the actual investigation would typically be carried out by law enforcement. The state health department (option c) may be involved if there are health-related concerns, but they would usually work in conjunction with law enforcement rather than leading the investigation. The resident's family (option d) may be concerned and may contact law enforcement to report the incident, but they would not be responsible for directing the investigation.