A nonparametric decentralized detection problem is investigated over tree-structured sensor networks, in which sensors are configured in trees with the fusion center being the root of the tree. A kernel-based classification approach is applied, which generalizes the approach initially proposed by Nguyen, Wainwright, and Jordan for single-level networks to tree networks. An algorithm for computing a jointly optimal decision rule for the fusion center and local decision rules for individual sensors are provided, which is based on a coordinate gradient algorithm. Furthermore, by exploiting the tree structure and choosing a suitable kernel function, a distributive protocol is proposed to distribute the computational loads to individual sensors for an efficient implementation of the optimization algorithm. Numerical simulations are provided to demonstrate that our algorithm achieves satisfactory accuracy in decision making for the cases with correlated and independent observations. It is also numerically demonstrated that our algorithm has a much smaller testing error than the likelihood-ratio based algorithm.