Recent advances in autonomous driving have raised the problem of safety to the forefront and incentivized research into establishing safety guarantees. In this paper, we propose a safety verification framework as a safety standard for driving controllers with full or shared autonomy based on compositional and contract-based principles. Our framework enables us to synthesize safety guarantees over entire road networks by first building a library of locally verified models, and then composing local models together to verify the entire network. Composition is achieved using assume-guarantee contracts that are synthesized concurrently during verification. Thus, we can reuse local models within and across networks, add additional models to cover local road geometries without re-verifying the entire library, and perform all computations in a parallel and distributed way, which enables computational tractability. Furthermore, we employ controller contracts such that any controller satisfying them can be certified safe. We demonstrate the practical effectiveness of our framework by certifying controllers over parts of the Manhattan road network.