In this paper, we consider a similarity control problem for nondeterministic discrete event systems, which requires us to synthesize a nonblocking supervisor such that the supervised plant is simulated by a given specification. We assume that a supervisor can observe not only the event occurrence but also the current state of the plant. We present a necessary and sufficient condition for the existence of a nonblocking supervisor that solves the similarity control problem and show how to verify it in polynomial time. Moreover, when the existence condition of a nonblocking supervisor is satisfied, we synthesize such a supervisor as a solution to the similarity control problem.