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Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance for medical image segmentation, yet need plenty of manual annotations for training. Semi-Supervised Learning (SSL) methods are promising to reduce the requirement of annotations, but their performance is still limited when the dataset size and the number of annotated images are small. Leveraging existing annotated datasets with similar anatomical structures to assist training has a potential for improving the model's performance. However, it is further challenged by the cross-anatomy domain shift due to the different appearance and even imaging modalities from the target structure. To solve this problem, we propose Contrastive Semi-supervised learning for Cross Anatomy Domain Adaptation (CS-CADA) that adapts a model to segment similar structures in a target domain, which requires only limited annotations in the target domain by leveraging a set of existing annotated images of similar structures in a source domain. We use Domain-Specific Batch Normalization (DSBN) to individually normalize feature maps for the two anatomical domains, and propose a cross-domain contrastive learning strategy to encourage extracting domain invariant features. They are integrated into a Self-Ensembling Mean-Teacher (SE-MT) framework to exploit unlabeled target domain images with a prediction consistency constraint. Extensive experiments show that our CS-CADA is able to solve the challenging cross-anatomy domain shift problem, achieving accurate segmentation of coronary arteries in X-ray images with the help of retinal vessel images and cardiac MR images with the help of fundus images, respectively, given only a small number of annotations in the target domain.