After one of the incidents, in Camborne on Monday, people needed hospital treatment, Cornwall Fire Service said.
Officers said gas appliances, open fires and wood-burning stoves could all be dangerous if not regularly serviced or swept.
All households should have carbon monoxide detectors, it added.
In the first incident, in Vyvyan Street, Camborne, two people were taken to hospital.
A second incident, in Bodmin, was due to be a defective flue on a wood burner, the service said.
Carbon monoxide cannot be seen, smelt or tasted.
Combustion appliances fuelled by solid fuel, oil or gas all have the potential to cause carbon monoxide poisoning if they are poorly installed or commissioned, inadequately maintained or incorrectly used.
At least 50 people die every year from carbon monoxide poisoning in the UK.