The same insurance coverage from your personal auto insurance policy will extend over to that rental car. So if you have comprehensive and collision coverage (commonly called full coverage) then your rental car will be repaired/replaced if it is damaged in your possession. You will be responsible for your deductible.
Rental car companies offer an add-on called collision damage waiver. By purchasing this waiver, any insurance claim would go through the rental car company – not your personal auto insurance. Typically, there is not a deductible if you purchase this waiver.
Of course, there are some restrictions on your personal auto insurance policy:
You will want to make sure that only the drivers on your personal auto policy are driving the rental car.
Most insurance companies have a limited number of days that you are covered to rent the car - usually it is 30 days.
Coverage will generally only apply in the U.S.
The rental car company can still choose to charge you for loss of use. Loss of use could apply if the vehicle is being repaired and they are unable to rent that vehicle out during that time period.
Each situation can be unique so please contact us with any specific questions.