Parkinson's disease is characterised by excessive subcortical beta oscillations. However, little is known about the functional connectivity of the two basal ganglia across hemispheres and specifically the role beta plays in this. We recorded local field potentials from the subthalamic nucleus bilaterally in 23 subjects with Parkinson's disease at rest, on and off medication. We found suppression of low beta power in response to levodopa (t22 = -4.4, p<0.001). There was significant coherence between the two sides in the beta range in 19 of the subjects. Coherence was selectively attenuated in the low beta range following levodopa (t22 = -2.7; p = 0.01). We also separately analysed amplitude co-modulation and phase synchronisation in the beta band and found significant amplitude co-modulation and phase locking values in 17 and 16 subjects respectively, off medication. There was a dissociable effect of levodopa on these measures, with a significant suppression only in low beta phase locking value (t22 = -2.8, p = 0.01) and not amplitude co-modulation. The absolute mean values of amplitude co-modulation (0.40±0.03) and phase synchronisation (0.29±0.02) off medication were, however, relatively low, suggesting that the two basal ganglia networks may have to be approached separately with independent sensing and stimulation during adaptive deep brain stimulation. In addition, our findings highlight the functional distinction between the lower and upper beta frequency ranges and between amplitude co-modulation and phase synchronization across subthalamic nuclei.