This paper investigates the performance of physical layer security (PLS) in a vehicle-to-vehicle (V2V) communication system, where a transmitter vehicle exploits a dual reconfigurable intelligent surface (RIS) to send confidential information to legitimate receiver vehicles under the non-orthogonal multiple access (NOMA) scheme in the presence of an eavesdropper vehicle. In particular, it is assumed that an RIS is near the transmitter vehicle and another RIS is close to the receiver vehicles to provide a wider smart radio environment. Besides, we suppose that the channels between two RISs suffer from the Fisher-Snedecor F fading model. Under this scenario, we first provide the marginal distributions of equivalent channels at the legitimate receiver vehicles by exploiting the central limit theorem (CLT). Then, in order to evaluate the PLS performance of the considered secure communication system, we derive analytical expressions of the average secrecy capacity (ASC), secrecy outage probability (SOP), and secrecy energy efficiency (SEE) by using the Gauss-Laguerre quadrature and the Gaussian quadrature techniques. Moreover, to gain more insights into the secrecy performance, the asymptotic expression of the ASC is obtained. The numerical results indicate that incorporating the dual RIS in the secure V2V communication under the NOMA scheme can significantly provide ultra-reliable transmission and guarantee more secure communication for intelligent transportation systems (ITS).