In genomic applications, there is often interest in identifying genes whose time-course expression trajectories exhibit periodic oscillations with a period of approximately 24 h (circadian genes). While it is natural to expect that the expression of gene i at time j might depend to some degree on the expression of the other genes measured at the same time, widely-used rhythmicity detection techniques do not accommodate for the potential dependence across genes. We develop a Bayesian approach for periodicity identification that explicitly takes into account the complex dependence structure across time-course trajectories in gene expressions. The methodology is applied to a plant gene expression dataset.