Recently, a proper bisimulation equivalence relation for random process model has been defined in a model independent approach. Model independence clarifies the difference between nondeterministic and probabilistic actions in concurrency and makes the new equivalence relation to be congruent. In this paper, we focus on the finite state randomized CCS model and deepen the previous work in two aspects. First, we show that the equivalence relation can be checked in polynomial time. Second, we give a sound and complete axiomatization system for this model. The algorithm and axiomatization system also have the merit of model independency as they can be easily generalized to the randomized extension of any finite state concurrent model.