Liability coverage:
Yes. If you have a personal car, your liability insurance will cover the rental car also. The rental company also has liability insurance, usually statutory minimum liability limits, which is insufficient to really protect you. The rental contract makes your own insurance primary. If you don’t have insurance, the rental company’s policy is primary.
You can buy additional non-owned vehicle liability coverage either directly with an agent or an insurance company. This may be a good idea if you don’t want an accident with the rental car to impact the premium rates on your personal vehicle policy. You may be able to buy additional liability coverage from the rental company, but it will be more expensive.
Physical damage coverage:
If you have collision and comprehensive coverage on your personal car, it will also apply to the rental car so that you won’t have to buy CDW/LDW. CDW/LDW is not insurance. It is a waiver of responsibility for damage to the rental car. It is not liability coverage for damage or injuries to third parties.
Your credit card company may also provide physical damage protection for a rental car. You must use that card to both rent and pay for the rental. Check with your credit card company to see if it provides this benefit.
Source: Quora