The industry encourages all hosts to have a carbon monoxide detector installed in the house as a safety precaution. This is for instances where there are gas appliances, indoor fireplaces or gas stoves inside the house. Most of our tiny house uses a portable hotplate as well as an induction cooker instead of gas cooker. Our hot water are gas heated, however, the gas cylinder is installed outside of the house and air is exhausted outside the house, not inside. We also use electric heater, not a fireplace in most of our tiny houses.
We do have a smoke detector installed in the tiny house to detect smoke in case there is fire. If you are worried, you may bring along a portable carbon monoxide detector as what Airbnb suggests, if this will help to give you a peace of mind.
That said, our smoke detector can be quite sensitive to smoke, so if you're cooking and producing a lot of steam, please do open up the windows for ventilation as it may set off the alarm.