UPDATED: Carbon monoxide alarm goes off while baking in oven

As a retired Fire Fighter I can advise you don't mess around with CO if you suspect a problem with the oven have it checked by a professional.
The only true way to accurately detect the level of CO present in an enclosed environment is with a multi gas meter that will read both the CO levels and O2 (oxygen) level within the confined space.
Your detector may be faulty but don't always assume. CO levels over 20 PPM (parts per million) are hazardous to your health. Over 100 PPM deadly.
Be safe and get things checks.