Single-case designs are experimental designs widely used in behavioral sciences, which involve only a single entity under observation. Traditionally these designs are analyzed through visual analysis techniques, but several different approaches have emerged. Among these approaches, permutation tests, also called randomization tests, deserve particular attention, because of the desirable property of being distribution free. In addition, they can be used to analyze different type of data and both univariate and multivariate problems. For this reason, we propose an extension of permutation tests to the analysis of a particular type of single-case designs, the completely randomized single-case designs, when the outcome is multivariate and ordinal. A simulation study is hence performed to evaluate the power of this testing procedure and a real application is also provided.