In this paper, we investigate a state-of-the-art reconfigurable intelligent surface (RIS)-assisted spatial scattering modulation (SSM) scheme for millimeter-wave (mmWave) systems, where a more practical scenario that the RIS is near the transmitter while the receiver is far from RIS is considered. To this end, the line-of-sight (LoS) and non-LoS links are utilized in the transmitter-RIS and RIS-receiver channels, respectively. By employing the maximum likelihood detector at the receiver, the conditional pairwise error probability (CPEP) expression for the RIS-SSM scheme is derived under the two scenarios that the received beam demodulation is correct or not. Furthermore, the union upper bound of average bit error probability (ABEP) is obtained based on the CPEP expression. Finally, the derivation results are exhaustively validated by the Monte Carlo simulations.