If a tree limb from my rental home fell on my car and damaged it who should pay?

Your car insurance would cover your damages.

A property owner is not liable for acts of nature anyways and home insurance policies do not cover automobiles.

AnswerYou would be responsible for the upkeep of the garden (and trees) unless there is something different specified in your lease. That would make you responsible for any damage caused by a falling limb. If your car is insured against accidental damage, then you could possibly make a claim as the earlier answer suggests. If not then you will have to pay for any repairs required.