You need CO2 detectors if you have any appliance that combusts a fuel within the house: mains gas, gas from a containner, wood, coal, anything you can think of.
Yes, a properly installed wood burner/balanced flue boiler, properly serviced should not cause any problems, but I used to work for British Gas in a job where I knew or read about all the the deaths caused by faulty appliances and saw all the information on grossly incompetently, badly installed appliances done by both fully qualified technicians and amateurs who thought they knew better and could save money by DIying it and that has made me absolutely meticulous about gaa safety including having more than 1 CO2 meter in my house to make absolutely sure we have protection to the highest level.