Combatting Anomalous Health Incidents Act This bill requires the Department of Defense (DOD) to brief Congress on anomalous health incidents affecting members of the Armed Forces and civilian DOD employees. In its briefing, DOD must address any ongoing efforts to protect members and employees from the effects of anomalous health incidents and the extent and nature of engagement by DOD with other federal departments and agencies regarding anomalous health incidents affecting their employees. The senior DOD official with the principal responsibility for leading the efforts regarding anomalous health incidents must be an official who is appointed by, and with the advice and consent of, the Senate.