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This paper presents the generalized Hausman test to detect non-normality of the latent variable distribution in unidimensional Item Response Theory (IRT) models for binary data. The test is based on the estimators resulting from the two-parameter IRT model, that assumes normality of the latent variable, and the semi-nonparametric IRT model, that assumes a more flexible latent variable distribution. The performance of the test is evaluated through a simulation study, including the cases where the latent variable is generated from a skew-normal and mixture of normals. The results highlight the good performance of the test when the latent variable is generated from a mixture of normals and from a skew-normal only with many items and large sample sizes.