A flexible model for analyzing multi-state panel count data is presented. Panel data here refers to observing the state of individuals or objects under observation at a discrete set of time points. Panel data is found in many disciplines such as the sciences and medicine. It is assumed that the data is being generated by a continuous time, discrete state space Markov process. The transition intensities are represented with model-based penalty smoothing. This provides a class of models ranging between a fully nonparametric and parametric assumption for the transition intensities. Estimation and inference of the proposed approach is outlined and the finite sample properties of the methodology investigated via simulation.