We propose a decentralized variant of Monte Carlo tree search (MCTS) that is suitable for a variety of tasks in multi-robot active perception. Our algorithm allows each robot to optimize its own actions by maintaining a probability distribution over plans in the joint-action space. Robots periodically communicate a compressed form of their search trees, which are used to update the joint distribution using a distributed optimization approach inspired by variational methods. Our method admits any objective function defined over robot action sequences, assumes intermittent communication, is anytime, and is suitable for online replanning.