In this work we look into the parallelization (in the NC sense) of the Markov Chain approach to almost random generation, as described by Sinclair (1993). We give a RNC almost uniform generator for perfect matchings in dense bipartite graphs, and its RNC reduction to its counting problem. As a consequence we can classify the problem of getting an approximation scheme to the permanent of a boolean matrix in RNC. We also state other problems for which the same technique applies.