In this paper we present a novel Markov Switching generative model for continuous multivariate time series and longitudinal data based on Gaussian copula functions. We assume that the values of the multivariate time series at every time slice are sampled out of a joint probability distribution that is selected by the latent state. The use of Gaussian copula functions give the flexibility of individual marginals for each time series and a common dependence structure given by a correlation matrix. The transition matrix together with all the observation models are learned by means of Gibbs sampling. We also test the method both with synthetic and real data sets, and compare them with other usual techniques. Results show that models assuming normality in real data sets are not a good approach when marginals are not Gaussian, and they are outranked by our proposal.