We investigate the computational complexity of the A* algorithm with reliability reordering, applied to maximum-likelihood (ML) decoding of block codes. Extensive computer simulations show that A* decoding with reliability reordering offers good average computational performance, but up to date there is no accurate analytical description of the decoding complexity. By using the theory of order statistics, we derive asymptotic bounds for the maximum decoding complexity as well as approximations for the average decoding complexity of the algorithm for large noise levels. The analysis shows that reordering is a key feature of the algorithm that allows for substantial computational savings.