In this paper, we study the impact and the improvement of using cooperative non-orthogonal multiple access scheme (NOMA) on a millimeter wave (mmWave) vehicular network at intersection roads. The intersections consists of two perpendicular roads. The transmission occurs between a source, and two destinations nodes with a help of a relay. We assume that the interference comes from as set of vehicles that are distributed as a one dimensional homogeneous Poisson point process (PPP). We derive closed form outage probability expressions for cooperative NOMA, and compare them with cooperative orthogonal multiple access (OMA). We show that, NOMA offers a significant improvement, especially for high data rates. However, there a condition imposed to the data rate, otherwise, the performance of NOMA will decreases dramatically. We show that as the nodes approach the intersection, the outage probability increases. Counter-intuitively, We show that, the non line of sigh (NLOS) scenario has a better performance than the line of sigh (LOS) scenario. The analysis is conducted using tools from stochastic geometry and is verified with Monte Carlo simulations.