In parametric copula setups, where both the marginals and the copula have parametric forms, two-stage maximum likelihood estimation, often referred to as inference function for margins, is used as an attractive alternative to the full maximum likelihood estimation strategy. With basic results derived earlier by the authors of the presentation, a copula information criterion (CIC) is developed. In a nutshell, CIC aims for the model that minimizes Kullback-Leibler divergence and doesn't assume that the chosen parametric model is the true model (i.e. data generating model), which is one of the core assumptions behind AIC. This implies that CIC is analogous to Takeuchi Information Criterion (TIC), which is defined for full maximum likelihood. When we make an assumption that the model is correctly specified, CIC simplifies to AIC. Further, since both CIC and TIC are estimating the same part of Kullback-Leibler divergence, they are compatible, in the sense that they can be used to compare the performance of full maximum-likelihood and two-stage maximum likelihood for a given model. We demonstrate the behavior of CIC by using a simulation study.