If you have an accident with a rental car, you can have secondary coverage with your credit card company if you charged your rental car use with a credit card and turned down the optional insurance with the car rental company. Credit cards give you secondary insurance coverage after your primary insurance company covers what it will cover for your accident. So, the credit card company should at least reimburse you for the deductible that you have to pay with your primary insurance company. Different credit card companies have different time limits, coverages, etc. You should check out each of your credit card coverages, and select the best one for your current needs before charging on one of your charge cards.
I personally had an accident in Arkansas, and my VISA credit card reimbursed me for the deductible that my primary coverage charged me, and also reimbursed me for the balance of the damage to the rental car that my primary insurance did not cover. So, the bottom line is that I ended up not paying any net out of pocket cost for this rental car accident.