This paper constructs and evaluates LM and Neyman's $C(\alpha)$ tests based on bivariate Edgeworth series expansions for the consistency of the Heckman's two-step estimator in sample selection models, that is, for marginal normality and linearity of the conditional expectation of the error terms. The proposed tests are robust to local misspecification in nuisance distributional parameters. Monte Carlo results show that testing marginal normality and linearity of the conditional expectations separately have a better size performance than testing bivariate normality. Moreover, the robust variants of the tests have better empirical size than non-robust tests, which determines that these tests can be successfully applied to detect specific departures from the null model of bivariate normality. Finally, the tests are applied to women's labor supply data.