Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.