Source-free domain adaptation (SFDA) aims to adapt a lightweight pretrained source model to unlabeled new domains without the original labeled source data. Due to the privacy of patients and storage consumption concerns, SFDA is a more practical setting for building a generalized model in medical object detection. Existing methods usually apply the vanilla pseudo-labeling technique, while neglecting the bias issues in SFDA, leading to limited adaptation performance. To this end, we systematically analyze the biases in SFDA medical object detection by constructing a structural causal model (SCM) and propose an unbiased SFDA framework dubbed decoupled unbiased teacher (DUT). Based on the SCM, we derive that the confounding effect causes biases in the SFDA medical object detection task at the sample level, feature level, and prediction level. To prevent the model from emphasizing easy object patterns in the biased dataset, a dual invariance assessment (DIA) strategy is devised to generate counterfactual synthetics. The synthetics are based on unbiased invariant samples in both discrimination and semantic perspectives. To alleviate overfitting to domain-specific features in SFDA, we design a cross-domain feature intervention (CFI) module to explicitly deconfound the domain-specific prior with feature intervention and obtain unbiased features. Besides, we establish a correspondence supervision prioritization (CSP) strategy for addressing the prediction bias caused by coarse pseudo-labels by sample prioritizing and robust box supervision. Through extensive experiments on multiple SFDA medical object detection scenarios, DUT yields superior performance over previous state-of-the-art unsupervised domain adaptation (UDA) and SFDA counterparts, demonstrating the significance of addressing the bias issues in this challenging task. The code is available at https://github.com/CUHK-AIM-Group/Decoupled-Unbiased-Teacher.