Reconfigurable intelligent surface (RIS) is a recently emerged promising technology for beyond-5G (B5G)/6G wireless networks. In this letter, we propose to employ a signal space diversity (SSD) technique to improve the performance of distributed RIS-aided dual-hop mixed radio frequency (RF)-free-space optical (FSO) communication systems. The source-relay, source-RIS, and RIS-relay links are assumed to undergo independent but not identically distributed (i.n.i.d.) Nakagami- $m$ fading. The destination node is equipped with multiple FSO apertures and the relay-destination links follow Gamma-Gamma (GG) distributed atmospheric turbulence (AT) model with pointing errors (PEs). Novel approximate closed-form expressions for the system’s symbol error rate (SER) are derived for both the exhaustive RIS-aided (ERA) and opportunistic RIS-aided (ORA) configurations. The numerical results show that using the SSD technique at both the RF and FSO links significantly improves the spectral efficiency and the diversity order of the system considered.