The complex system response of 3D position-sensitive gamma-ray detectors complicates modeling the recorded measurements and makes exact expressions for detection performance intractable. This makes source detection performance difficult and expensive to compute. Asymptotic analysis has the potential to simplify detection performance prediction with complex systems and has previously been applied to detection performance prediction with simulated gamma-ray detectors. In this work, we use asymptotic performance prediction methods to predict points on the receiver operating characteristic (ROC) curve for the illustrative task of detecting a 137Cs source in background with an 18-detector CdZnTe array. We assume that the source position, source energy, background spectrum, and background spatial distribution are known. Although these assumptions are not always valid in practice, the efficiency of the prediction method makes it attractive for detection system design problems. Our results show that the asymptotic performance prediction method accurately predicts the empirically observed performance with real data recorded with a real system. Our results also characterize the performance of the detector array for the task of source detection. The accuracy and computational efficiency of the asymptotic detection performance prediction method make it a viable alternative to empirical performance evaluation.