Integrated sensing and communication (ISAC) is expected to play a prominent role among emerging technologies in future wireless communications. In particular, a communication radar coexistence system is degraded significantly by mutual interference. In this work, given the advantages of promising reconfigurable intelligent surface (RIS), we propose a simultaneously transmitting and reflecting RIS (STAR-RIS)-assisted radar coexistence system where a STAR-RIS is introduced to improve the communication performance while suppressing the mutual interference and providing full space coverage. Based on the realistic conditions of correlated fading, and the presence of multiple user equipments (UEs) at both sides of the RIS, we derive the achievable rates at the radar and the communication receiver side in closed forms in terms of statistical channel state information (CSI). Next, we perform alternating optimization (AO) for optimizing the STAR-RIS and the radar beamforming. Regarding the former, we optimize the amplitudes and phase shifts of the STAR-RIS through a projected gradient ascent algorithm (PGAM) simultaneously with respect to the amplitudes and phase shifts of the surface for both energy splitting (ES) and mode switching (MS) operation protocols. The proposed optimization saves enough overhead since it can be performed every several coherence intervals. This property is particularly beneficial compared to reflecting-only RIS because a STAR-RIS includes the double number of variables, which require increased overhead. Finally, simulation results illustrate how the proposed architecture outperforms the conventional RIS counterpart, and show how the various parameters affect the performance. Moreover, a benchmark full instantaneous CSI (I-CSI) based design is provided and shown to result in higher sum-rate but also in large overhead associated with complexity.