A parallel design, in which items across different scales within an instrument share common stimuli and subjects respond to the common stimulus for each scale, is sometimes used in questionnaires or inventories. Because the items across scales share the same stimuli, the assumption of local item independence may not hold, thereby violating the assumption of local item independence under standard psychometric models. In this study, the authors describe a multidimensional item response model to detect specific forms of local item dependence. Three real data sets were analyzed to illustrate implications and applications of the proposed method.