In this paper, we study the performance of millimeter wave (mmWave) vehicular communications (VCs) using non-orthogonal multiple access scheme (NOMA) at road intersections, since there areas are more prone to accidents. We study the case when the intersection involves two perpendicular lanes, we then extend the study to an intersection with several lanes. The transmission occurs between a source, and two destinations. The transmission experiences interference originated from a set of vehicles that are distributed as a Poisson point process (PPP). Our analysis includes the effects of blockage from buildings and vehicles at intersections. Closed form outage probability expressions are obtained. We show that as the nodes reach 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. Finally, we compare the performance of mmWave NOMA with OMA, and we show that NOMA offers a significant improvement over OMA mmWave vehicular networks. The analysis is verified by Monte-Carlo simulation.