Under the assumption of multivariate normality Rao's score test is utilized to test the hypothesis that a covariance matrix has a double exchangeable structure, i.e., three-level array-variate data obey a nested rotational invariant covariance structure. The alternative hypothesis assumes an unstructured covariance matrix. An advantage of Rao's score test is that one does not have to estimate parameters under both the null and alternative hypothesis: Rao's score test can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test cannot be. Simulation studies are performed to study the effects of sample sizes, and to estimate empirical percentiles of Rao's score test statistic, under the null hypothesis. The test is investigated with three real datasets.