We propose decision algorithms for bisimulation relations defined on probabilistic automata, a model for concurrent nondeterministic systems with randomization. The algorithms decide both strong and weak bisimulation relations based on deterministic as well as randomized schedulers. These algorithms extend and complete other known algorithms for simpler relations and models. The algorithm we present for strong probabilistic bisimulation has polynomial time complexity, while the algorithm for weak probabilistic bisimulation is exponential; however we argue that the latter is feasible in practice.