Inspired by Connected-UNets, this study proposes a deep learning model, called Connected-SegNets, for breast tumor segmentation from X-ray images. In the proposed model, two SegNet architectures are connected with skip connections between their layers. Moreover, the cross-entropy loss function of the original SegNet has been replaced by the intersection over union (IoU) loss function in order to make the proposed model more robust against noise during the training process. As part of data preprocessing, a histogram equalization technique, called contrast limit adapt histogram equalization (CLAHE), is applied to all datasets to enhance the compressed regions and smooth the distribution of the pixels. Additionally, two image augmentation methods, namely rotation and flipping, are used to increase the amount of training data and to prevent overfitting. The proposed model has been evaluated on two publicly available datasets, specifically INbreast and the curated breast imaging subset of digital database for screening mammography (CBIS-DDSM). The proposed model has also been evaluated using a private dataset obtained from Cheng Hsin General Hospital in Taiwan. The experimental results show that the proposed Connected-SegNets model outperforms the state-of-the-art methods in terms of Dice score and IoU score. The proposed Connected-SegNets produces a maximum Dice score of 96.34% on the INbreast dataset, 92.86% on the CBIS-DDSM dataset, and 92.25% on the private dataset. Furthermore, the experimental results show that the proposed model achieves the highest IoU score of 91.21%, 87.34%, and 83.71% on INbreast, CBIS-DDSM, and the private dataset, respectively.