Unsupervised domain adaptive object detection (UDA-OD) is a challenging task that aims to improve the generalization of detectors across domains. Although the existing UDA-OD methods have demonstrated their capabilities, they fail to investigate two critical correlations in the adaptation procedure, i.e., 1) the correlation between the features inside an image and 2) the correlation between the domain-invariant and domain-specific features across domains. To take full advantage of these two correlations, we propose a Cyclic Reconstruction and Decoupling Adaptation (CRADA) framework to efficiently decouple and align the features from different domains. Our CRADA builds graphs for images to capture the correlation between the informative points, and decouples it into two components, one for the domain-specific features and the other for the domain-invariant features. To enhance the qualities of the decoupled features, we also propose a cyclic decoupling-reconstruction-decoupling strategy and a swap-and-reconstruction procedure for the decoupled features of different domains. To make the training procedure easier, we introduce a confidence-guided update scheme for the memory bank and overcome the problem of asymmetric categories in each training batch. We conduct comprehensive experiments to verify the effectiveness of our proposed CRADA.