In this work, we consider the use of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to assist the communication between the access point (AP) and two users, along with the existence of direct links. Considering the non-orthogonal multiple access (NOMA) based transmission by AP, we derive the expressions for coverage probability of both the users assuming Nakagami-m fading channels with the possibility of imperfect successive interference cancellation (SIC) at the near user. We also find the optimal values of NOMA power allocation parameter and STAR-RIS transmission coefficient that jointly minimizes the absolute difference in the throughput of the two users. The superiority of the proposed system is shown through numerical results in contrast to a STAR-RIS assisted orthogonal multiple access (OMA) transmission and a conventional NOMA scheme. The impact of various other system parameters like number of reflecting elements and fraction of imperfect SIC is demonstrated on the system performance.