The basal ganglia (BG) play an important role in motor control, reinforcement learning, and perceptual decision making. Modeling and experimental evidence suggest that, in a speed-accuracy tradeoff, the corticostriatal pathway can adaptively adjust a decision threshold (the amount of information needed to make a choice). In this study, we go beyond the focus of previous works on the direct and hyperdirect pathways to examine the contribution of the indirect pathway of the BG system to decision making in a biophysically based spiking network model. We find that the mechanism of adjusting the decision threshold by plasticity of the corticostriatal connections is effective, provided that the indirect pathway counterbalances the direct pathway in their projections to the output nucleus. Furthermore, in our model, changes within basal ganglia connections similar to those that arise in parkinsonism give rise to strong beta oscillations. Specifically, beta oscillations are produced by an abnormal enhancement of the interactions between the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe) in the indirect pathway, with an oscillation frequency that depends on the excitatory cortical input to the STN and the inhibitory input to the GPe from the striatum. In a parkinsonian state characterized by pronounced beta oscillations, the mean reaction time and range of threshold variation (a measure of behavioral flexibility) are significantly reduced compared with the normal state. Our work thus reveals a specific circuit mechanism for impairments of perceptual decision making associated with Parkinson's disease.