Tumor segmentation in multimodal medical images has seen a growing trend towards deep learning based methods. Typically, studies dealing with this topic fuse multimodal image data to improve the tumor segmentation contour for a single imaging modality. However, they do not take into account that tumor characteristics are emphasized differently by each modality, which affects the tumor delineation. Thus, the tumor segmentation is modality- and task-dependent. This is especially the case for soft tissue sarcomas, where, due to necrotic tumor tissue, the segmentation differs vastly. Closing this gap, we develop a modalityspecific sarcoma segmentation model that utilizes multimodal image data to improve the tumor delineation on each individual modality. We propose a simultaneous co-segmentation method, which enables multimodal feature learning through modality-specific encoder and decoder branches, and the use of resource-effcient densely connected convolutional layers. We further conduct experiments to analyze how different input modalities and encoder-decoder fusion strategies affect the segmentation result. We demonstrate the effectiveness of our approach on public soft tissue sarcoma data, which comprises MRI (T1 and T2 sequence) and PET/CT scans. The results show that our multimodal co-segmentation model provides better modality-specific tumor segmentation than models using only the PET or MRI (T1 and T2) scan as input.