Every large census operation should undergo evaluation programs to find the sources and extent of inherent coverage errors. In this article we briefly discuss the statistical methodology to estimate the omission rate in Indian census using Dual System Estimation (DSE) technique. We have explicitly studied the correlation bias factor involved in the estimate, its extent and consequences. A new potential source of bias in the estimate is identified and discussed. During the survey, more efficient enumerators compared to the census operations are appointed and this fact may inflate the dependency between two lists and lead to a significant bias. Some examples are given to demonstrate this argument in various plausible situations. We have suggested one simple and flexible approach which can control this bias. Our proposed estimator can efficiently overcome the potential bias by achieving desired degree of accuracy(almost unbiased) with relatively higher efficiency. Overall improvements in the results are explored through simulation study on different populations.