This study explores the performance of a cooperative non-orthogonal multiple access (CNOMA) downlink wireless communication system, aided by a novel technology called si- multaneously transmitting and reflecting re- configurable intelligent surfaces (STAR-RISs), operating over Nakagami-m fading channels. The evaluation focuses on outage probability (OP), spectral efficiency (SE), and energy effi- ciency (EE) as key performance indicators. The mathematically intractable probability density and cumulative distribution functions of the near user are approximated using the Gamma moment-matching method. This enables the derivation of closed-form expressions for OP and ergodic rates of users, which are used to determine SE and EE. Monte-Carlo simulations validate the analytical results. A comparison with OMA and NOMA is provided to assess CNOMA’s effectiveness, revealing that the co- operative link can enhance SE and EE in the STAR-RIS-based NOMA network.