While connected vehicle (CV) applications have the potential to revolutionize traditional transportation system, cyber and physical attacks on them may lead to disastrous consequences. In this work, we propose an efficient dual cyber-physical blockchain framework to build trust and secure communication for CV applications. Our approach incorporates blockchain technology and physical sensing capabilities of vehicles to quickly react to attacks in a large-scale vehicular network, with low resource overhead. We explore the application of our framework to three CV applications, i.e., highway merging, intelligent intersection management, and traffic network with route choices. Simulation results demonstrate the effectiveness of our blockchain-based framework in defending against spoofing attacks, bad mouthing attacks, and Sybil and voting attacks. We also provide analysis to show the timing and resource efficiency of our framework.