Most of the Cleveland Hopkins Intl Airport car hire agencies do allow you to have your furry friends with you while you make use of your hire car. However, your pet needs to be kept in a safe travel cage/box while in the car. They are not allowed to roam free! It is also your responsibility to make sure the car is properly cleaned with no trace of your pet in the car; for example, its fur must be removed to avoid any additional cleaning the agency feels is necessary, which they will charge you for. Search car hire on KAYAK