Is there a significant risk of CO2 buildup with a ductless heat pump A/C?
Your house is not a space-ship, and it's not built like a space-ship. 

If it's built anywhere close to a spaceship, you can run continuous ventilation fans, typically though an air-air heat exchanger. If it's of "normal construction" normal leakage will take care of adequate air exchange.

If you are adequately curious you can have a "blower door test" done to determine the actual leakage rate of your house under controlled conditions, which might inform both sealing particular leakage areas and the decision of whether or not to install active ventilation.