Unsupervised Domain Adaptive (UDA) person search focuses on employing the model trained on a labeled source domain dataset to a target domain dataset without any additional annotations. Most effective UDA person search methods typically utilize the ground truth of the source domain and pseudo labels derived from clustering during the training process for domain adaptation. However, the performance of these approaches will be significantly restricted by the disrupting pseudo labels resulting from inter-domain disparities. In this paper, we propose a Dual Self-Calibration (DSCA) framework for UDA person search that effectively eliminates the interference of noisy pseudo labels by considering both the image-level and instance-level features perspectives. Specifically, we first present a simple yet effective Perception-Driven Adaptive Filter (PDAF) to adaptively predict a dynamic filter threshold based on input features. This threshold assists in eliminating noisy pseudo boxes and other background interference, allowing our approach to focus on foreground targets and avoid indiscriminate domain adaptation. Besides, we further propose a Cluster Proxy Representation (CPR) module to enhance the update strategy of cluster representation, which mitigates the pollution of clusters from misidentified instances and effectively streamlines the training process for unlabeled target domains. With the above design, our method can achieve state-of-the-art (SOTA) performance on two benchmark datasets, with 80.2\% mAP and 81.7\% top-1 on the CUHK-SYSU dataset, with 39.9\% mAP and 81.6\% top-1 on the PRW dataset, which is comparable to or even exceeds the performance of some fully supervised methods.