No, you don't need extra insurance. The coverage on your vehicle extends to the rental. However, all states differ. There are some that say the rental car's liability insurance is primary and that yours is secondary. There are often disagreements between insurance companies, whose contracts put them excess over the rental company, and the rental company, who tries to put your insurance first. What matters is what the statutes say about whether rentals have to have insurance on them and how the law sees it. Either way, if you have your own insurance, and there's insurance on the rental, it will get sorted out.