rental car accident

Right before the christmas, my rental car was hit by another car in another state. we called the police. since the accident was happended at the gas station, the police said that he couldn't write a police report. but he helped us exchanged information, and gave us a reference number for his "record". both rental car and the other car were lightly damaged(need repair). my rental car was stopped behind the other car while the other car backed up and hit my car. I think it was the other car's fault. I wrote the accident report to the rental car company along with other car's info and police's info. the custom service person told me that they would contact me in the future. my hu*****and and I did not buy the rental car's insurance, and our own insurance won't cover it, but my hu*****and's credit card should cover it (it rented under his name, but since i am the spouse, i was told to allow to drive it, however, my name was not on the contract). we had returned the car for a week, do you think we should contact the other car's insurance company?