Recognising dialogue acts (DA) is important for many natural language processing tasks such as dialogue generation and intention recognition. In this paper, we propose a dual-attention hierarchical recurrent neural network for DA classification. Our model is partially inspired by the observation that conversational utterances are normally associated with both a DA and a topic, where the former captures the social act and the latter describes the subject matter. However, such a dependency between DAs and topics has not been utilised by most existing systems for DA classification. With a novel dual task-specific attention mechanism, our model is able, for utterances, to capture information about both DAs and topics, as well as information about the interactions between them. Experimental results show that by modelling topic as an auxiliary task, our model can significantly improve DA classification, yielding better or comparable performance to the state-of-the-art method on three public datasets.