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Non-random sample selection arises when observations do not come from a random sample. Instead, individuals select themselves into (or out of) the sample on the basis of observed and unobserved characteristics. In this case, estimates obtained using standard methods such as linear or logistic regression will be biased and inconsistent. This problem can be addressed using sample selection models. In the methodological literature a lot of attention has been given to sample selection models with continuous response. At the same time, not much work has been attributed to sample selection models with count response. The aim of this project is to develop a copula-based sample selection model for count data with flexible covariate effects. First, the literature on sample selection models will be reviewed. Second, two motivating data sets originating from the German Socio-Economic Panel (SOEP) and the United States Veterans' Administration (VA) will be described and explored. Third, the parametric count sample selection model will be depicted. Fourth, flexible covariate effects will be introduced together with inferential and model selection methods. Fifth, the model will be illustrated on the previously mentioned data sets. Finally, potential extensions for future research will be discussed.