Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Lof test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte Carlo test approach to p value computation is proposed and is shown to yield a powerful test. Repeated and sequential Monte Carlo tests that can greatly reduce computing time are discussed. (Contains 2 tables and 2 figures.)