Maximum likelihood (ML) estimator to Christofides model (CD) is presented to estimate proportion from randomized response (RR) data. Application of the EM algorithm to Christofides model is presented to compute the ML estimate for this proportion, especially when CD and ML methods give estimates outside the range . It is shown that one can apply the EM algorithm by viewing the observations from RR procedures as incomplete data. A general formulation of EM algorithm is sketched for CD. The simulation technique is used to generate a number of numerical applications, based on well-established Christofides design for estimating this proportion to illustrate the procedures