In empirical use of Mokken scaling, the $Crit$ index is used as evidence (or lack thereof) of violations of some common model assumptions. The main goal of our study was two-fold: To make the formulation of the $Crit$ index explicit and accessible, and to investigate its distribution under various measurement conditions. We conducted two simulation studies in the context of dichotomously-scored item responses. False positive rates and power to detect assumption violations were considered. We found that the false positive rates of $Crit$ were close to the nominal rate in most conditions, and that power to detect misfit depended on the sample size, type of violation, and number of assumption-violating items. Our findings are relevant to all practitioners who use Mokken scaling for scale and questionnaire construction and revision.