In practice, some coefficients in generalised varying coefficient models may be constant. We pay a price on the variance side of an estimator when constant coefficients are treated as special functions. This prompts the question of how to identify the constant coefficients. This is basically a model selection problem. In this paper, we use cross-validation (CV) as a criterion for model selection to identify the constant coefficients. We investigate the asymptotic properties of the proposed CV-based model selection approach. We report on a simulation study conducted to show how well the proposed method works when sample size is finite. Finally, the proposed method is used to analyse a data set from China about contraceptive use, which leads to some interesting findings.