This paper proposes a novel partial non-orthogonal multiple access (P-NOMA)-based semi-integrated sensing and communication (ISaC) system design. As an example ISaC scenario, we consider a vehicle simultaneously receiving the communication signal from infrastructure-to-vehicle (I2V) and sensing signal from vehicle-to-vehicle (V2V). P-NOMA allows exploiting both the orthogonal multiple access (OMA) and NOMA schemes for interference reduction and spectral efficiency (SE) enhancement while providing the flexibility of controlling the overlap of the sensing and communication signals according to the channel conditions and priority of the sensing and communication tasks. In this respect, we derive the closed-form expressions for communication outage probability and sensing probability of detection in Nakagami-m fading by considering the interference from the composite sensing channel. Our extensive analysis allows capturing the performance trade-offs of the communication and the sensing tasks with respect to various system parameters such as overlapping partial NOMA parameter, target range, radar cross section (RCS), and parameter m of the Nakagami-m fading channel. Our results show that the proposed P-NOMA-based semi-ISaC system outperforms the benchmark OMA-and NOMA-based systems in terms of communication spectral efficiency and probability of detection for the sensing target.