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We study the coarse-grained selection module in retrieval-based chatbot. Coarse-grained selection is a basic module in a retrieval-based chatbot, which constructs a rough candidate set from the whole database to speed up the interaction with customers. So far, there are two kinds of approaches for coarse-grained selection module: (1) sparse representation; (2) dense representation. To the best of our knowledge, there is no systematic comparison between these two approaches in retrieval-based chatbots, and which kind of method is better in real scenarios is still an open question. In this paper, we first systematically compare these two methods from four aspects: (1) effectiveness; (2) index stoarge; (3) search time cost; (4) human evaluation. Extensive experiment results demonstrate that dense representation method significantly outperforms the sparse representation, but costs more time and storage occupation. In order to overcome these fatal weaknesses of dense representation method, we propose an ultra-fast, low-storage, and highly effective Deep Semantic Hashing Coarse-grained selection method, called DSHC model. Specifically, in our proposed DSHC model, a hashing optimizing module that consists of two autoencoder models is stacked on a trained dense representation model, and three loss functions are designed to optimize it. The hash codes provided by hashing optimizing module effectively preserve the rich semantic and similarity information in dense vectors. Extensive experiment results prove that, our proposed DSHC model can achieve much faster speed and lower storage than sparse representation, with limited performance loss compared with dense representation. Besides, our source codes have been publicly released for future research.