In this paper we discuss inferential aspects and the local influence analysis of the multivariate null intercept measurement error model where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. In order to develop the hypotheses testing of interest and the local influence diagnostics, closed-form expressions of the marginal likelihood, the score function and the observed information matrix are presented. Additionally, an EM-type algorithm for evaluating the unrestricted and restricted maximum likelihood estimates of the parameters under equality constraints on the regression coefficients is examined. Also, we derive the appropriate matrices to assess the local influence on the parameters estimate under different perturbation schemes. The results and methods are applied to a dental clinical trial presented in Hadgu and Koch [Journal of Biopharmaceutical Statistic 9 (1999) 161–178].