Considering a simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS)-aided dual-functional radar-communications (DFRC) system, this paper proposes a symbol-level precoding-based scheme for enhancing the physical layer (PHY) security of the confidential information transmission and performing target sensing simultaneously. Specifically, the STAR-RIS-aided DFRC system design objective is to maximize the average received radar sensing power subject to the quality-of-service constraints for multiple communication users, the security constraint for multiple potential eavesdroppers, as well as various practical waveform design restrictions. However, the formulated problem is challenging to handle due to its nonconvexity. To address these issues, we propose a distance-majorization induced low-complexity algorithm to obtain an efficient solution. Simulation results confirm the effectiveness of the STAR-RIS in improving the DFRC performance.