In this letter, the performance of reconfigurable intelligent surface (RIS)-assisted non-orthogonal multiple access (NOMA) system is studied in the cooperative scenarios, where the quality of the received signals for the far user is enhanced by the assistance of the near user. We respectively derive the exact closed-form expressions for the outage probabilities of near user and far user under Nakagami-m fading. Further, to give more insights into the system performance, the asymptotic outage probability is obtained at the high signal-to-noise ratio (SNR) regime. The results show that the near user can achieve a diversity order of m, while the far user can achieve a diversity order relating to a and m, where m denotes the shape parameter of Nakagami-m distribution, and a is a function of m and the number of reflecting elements N. Simulation result are provided to verity the theoretical analysis.