For medical students, virtual patient dialogue systems can provide useful training opportunities without the cost of employing actors to portray standardized patients. This work utilizes word- and character-based convolutional neural networks (CNNs) for question identification in a virtual patient dialogue system, outperforming a strong word- and character-based logistic regression baseline. While the CNNs perform well given sufficient training data, the best system performance is ultimately achieved by combining CNNs with a hand-crafted pattern matching system that is robust to label sparsity, providing a 10% boost in system accuracy and an error reduction of 47% as compared to the pattern-matching system alone.