Random link but it lists clothes dryers as being a source of carbon monoxide
https://www.health.state.mn.us/communities/environment/air/toxins/index.html
Context.
Yes, it is a
source (because it burns gas!), but as stated, if working properly, it will all get vented outside, it won't contribute CO to
inside your home.
In fact,
it should reduce CO in your home, as it is sucking in air and expelling it. So any CO created by, say a gas stove (which isn't vented), will be part of the air the dryer is expelling, and will be replaced with fresh air (that naturally leaks into your home).
Added safety point: In addition the the comments that you must make sure your dryer exhaust is clear, so it exhausts w/o backup - you must also be sure there is a source of make-up air for the dryer.
Our dryer is in a 'mud room' hall between garage door and hall into the home. It has an air register/vent in the wall that connects that small room to the rest of the house. I realized that is so that if both doors are closed to the mud room, the dryer still can get air.
If you look at building codes, a gas dryer, furnace, water heater will all need exposure to X cubic feet of room air. If the rooms are too small, some kind of vent to the outside is required. I've thought about adding a vent in that room to the outside, so it isn't sucking conditioned air when the heat or AC is running, but it's not convenient, and the next owner would wonder what the heck this register with a cover plate is for.
-ERD50