Traditional hidden Markov models have been a useful tool to understand and model stochastic dynamic data; in the case of non-Gaussian data, models such as mixture of Gaussian hidden Markov models can be used. However, these suffer from the computation of precision matrices and have a lot of unnecessary parameters. As a consequence, such models often perform better when it is assumed that all variables are independent, a hypothesis that may be unrealistic. Hidden Markov models based on kernel density estimation are also capable of modeling non-Gaussian data, but they assume independence between variables. In this article, we introduce a new hidden Markov model based on kernel density estimation, which is capable of capturing kernel dependencies using context-specific Bayesian networks. The proposed model is described, together with a learning algorithm based on the expectation-maximization algorithm. Additionally, the model is compared to related HMMs on synthetic and real data. From the results, the benefits in likelihood and classification accuracy from the proposed model are quantified and analyzed.