Good question, but ask the rental company instead of us.
And for pete's sake, read the rental contract. Usually you'll be OK if the other driver is at fault and has insurance and all that, but read the contract anyway. There may be something in there that says you're responsible for any applicable deductibles or down-time of the vehicle, and if you sign the contract you're on the hook. If you can't understand the contract, ask the rental company to explain it to you before you sign.
NOTE: It's not just accidents you need to worry about. When you rent a car, you also agree that you are personally responsible for ANY damage that happens to it - regardless of fault. That's why their collision insurance at the counter is so expensive - but it usually covers pretty much everything and places little if any responsibility on you.
Know your responsibilities, know the risks, and know your options.