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Recent proposed approaches have made promising progress in dialogue state tracking (DST). However, in multi-domain scenarios, ellipsis and reference are frequently adopted by users to express values that have been mentioned by slots from other domains. To handle these phenomena, we propose a Dialogue State Tracking with Slot Connections (DST-SC) model to explicitly consider slot correlations across different domains. Given a target slot, the slot connecting mechanism in DST-SC can infer its source slot and copy the source slot value directly, thus significantly reducing the difficulty of learning and reasoning. Experimental results verify the benefits of explicit slot connection modeling, and our model achieves state-of-the-art performance on MultiWOZ 2.0 and MultiWOZ 2.1 datasets.