We investigate the problem of coordinating two robot arms to solve non-monotone tabletop multi-object rearrangement tasks. In a non-monotone rearrangement task, complex object-object dependencies exist that require moving some objects multiple times to solve an instance. In working with two arms in a large workspace, some objects must be handed off between the robots, which further complicates the planning process. For the challenging dual-arm tabletop rearrangement problem, we develop effective task planning algorithms for scheduling the pick-n-place sequence that can be properly distributed between the two arms. We show that, even without using a sophisticated motion planner, our method achieves significant time savings in comparison to greedy approaches and naive parallelization of single-robot plans.