While I can see such documentation for the business that owns the car, I can't find anything that clarifies that for a rental vehicle. I mean, a car rental service does annotate starting/ending miles for each client that rents from them. But they don't ask for the purpose of use, list of destinations and all that stuff. The car is more of a business asset to the rental company that is used to generate income for that rental business.
But while keeping more detailed records of my personal use for my business (which is the owner of the vehicle) I'd only see the need to document mileage only for the entity renting the vehicle from me. Just the mileage when it left the lot, and the mileage when it returned. Don't know what good that would do unless I was charging rent at a per-mile rate. But I'd do that anyway.
