Local dependence (LD) refers to the violation of the local independence assumption of most item response models. Statistics that indicate LD between a pair of items on a test or questionnaire that is being fitted with an item response model can play a useful diagnostic role in applications of item response theory. In this paper a new score test statistic, S?b?, for underlying LD (ULD) is proposed based on the bifactor 2-parameter logistic model. To compare the performance of S?b? with the score test statistic (St) based on a threshold shift model for surface LD (SLD), and the LD X2 statistic, we simulated data under null, ULD, and SLD conditions, and evaluated the null distribution and power of each of these test statistics. The results summarize the null distributions of all three diagnostic statistics, and their power for approximately matched degrees of ULD and SLD. Future research directions are discussed, including the straightforward generalization of Sb for polytomous item response models, and the challenges involved in the corresponding generalizations of St and LD X2.