Does my car insurance policy cover when I drive rental car?

Yes, your car insurance policy cover you when you drive rental car. Some people need extra insurance when they rent a car which depends on two things: your auto insurance policy coverage and your credit card.
If you have comprehensive and Collision coverage which pays for damages like scratches, dents and thefts, then this coverage may transfer to a rental car. Many credit cards may also pay for the damage caused to a rental car when you pay with that card, but the coverage may be secondary to your own policy if you have one. Credit card may also pay for towing but not for damage or injury that you cause to another car or driver.
Some companies also provide coverage for their employees who rent cars,so before going with the coverage first check with your boss.
If you purchase insurance from the rental car company, then you have several benefits like no deductible, no hassle of filing a claim, etc.