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A credal classifier for multilabel data is presented. This is obtained as an extension of Zaffalon's naive credal classifier to the case of non-exclusive class labels. The dependence relations among the labels are shaped with a tree topology. The classifier, based on a polynomial-time algorithm to compute whether or not a class label is optimal, returns a compact description of the set of optimal sequences of labels. Extensive experiments on real multilabel data show that the classifier gives more robust predictions than its Bayesian counterpart. In practice, when multiple sequences are returned in output, the Bayesian model is more likely to be inaccurate, while the sequences returned by the credal classifier are more likely to include the correct one.