If you have Full Coverage on your current vehicle, (in other words, your personal car is covered and would be repaired if you get in an accident), then Yes, you have coverage for damage to the rental car.
However, the rental car companies are now stating that if the rental car you damage is out of service for repairs, they may have the option to charge you for “loss of income” for the days the vehicle is not able to be rented out. (I have yet to see this happen, but please be aware that this is possible) There is no coverage for “loss of income” to the rental car company. Your policy coverages will transfer to the car, and repair it if needed, but will not cover charges for lost income.
Now, if you have Liability Only coverage (no coverage for comp or collision), then you DO NOT have any type of coverage for a rental car and you should consider purchasing coverage from the rental car company.
How do you find out what coverages you have?
Your current coverages are listed on your policy declarations page. Where is that you might ask? Most likely filed away in a file cabinet or probably tossed in the garbage bin. (I hope not, but probably)
If your insurance company has an online portal, you should be able to look it up.
You can always call your agent and review your coverages with him/her.
Either way, it’s important to know what coverages you have BEFORE you get your rental car. That way you’ll know if you should pony up the extra dough for the rental car insurance.