The problem of testing the separability of a covariance matrix against an unstructured variance covariance matrix in the context of multivariate repeated measures data is studied. Rao's score test (RST) statistic [1] is developed with the first component as an autoregressive of order one (AR(1))correlation matrix for this purpose under the as-sumption of multivariate normality. Simulation studies are conducted for the purpose of sample size consideration, and for the estimation of empirical percentiles of the null dis-tribution of RST statistic as well as that of the likelihood ratio test statistic. Both tests are implemented with data sets from medical studies.