According to the Nevada Legislature's website, AB 511 "revis[ing] certain provisions governing transportation" passed the Assembly (36-6) and the Senate (20-1) and was signed into law by the governor this week.
Although I am aware of no law that prohibits driverless cars, this appears to be the first law officially to sanction the technology. Specifically, the law provides that the Nevada Department of Transportation "shall adopt regulations authorizing the operation of autonomous vehicles on highways within the State of Nevada." The law charges the Nevada DOT with setting safety and performance standards and requires it to designate areas where driverless cars may be tested. (Note that this could take some serious time: Japan, for instance, has been promising standards for personal robots for years and has yet to release them.)