When the renter takes your car you will need to provide him/her with your car documentation which you would have on you if you would drive the car yourself. It is not allowed to only have a copy of the car documentation.
This is not specifically mentioned in the check-in procedure, it is your own responsibility to make sure the renter has the right documents to drive in your car.
In some cases it is necessary for the renter to also have the so called Green Card when he/she is going abroad. Please read this article for more information about the Green Card and how to apply for it.