The standard multiple imputation technique focuses on parameter estimation. In this study, we describe a method for conducting score tests following multiple imputation. As an important application, we use the Cochran‐Mantel‐Haenszel (CMH) test as a score test and compare the proposed multiple imputation method with a method based on the Wilson‐Hilferty transformation of the CMH statistic. We show that the proposed multiple imputation method preserves the nominal significance level for three types of alternative hypotheses, whereas that based on the Wilson‐Hilferty transformation inflates type I error for the “row means differ” and “general association” alternative hypotheses. Moreover, we find that this type I error inflation worsens as the amount of missing data increases.