We propose a decentralised 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 optimise its own individual action space by maintaining a probability distribution over plans in the joint-action space. Robots periodically communicate a compressed form of these search trees, which are used to update the locally-stored joint distributions using an optimisation approach inspired by variational methods. Our method admits any objective function defined over robot actions, assumes intermittent communication, and is anytime. We extend the analysis of the standard MCTS for our algorithm and characterise asymptotic convergence under reasonable assumptions. We evaluate the practical performance of our method for generalised team orienteering and active object recognition using real data, and show that it compares favourably to centralised MCTS even with severely degraded communication. These examples support the relevance of our algorithm for real-world active perception with multi-robot systems.