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We consider a local post-stratification approach to analyze the capture–recapture dual system Accuracy and Coverage Evaluation (A.C.E.) data associated with the 2000 U.S. Census. The local post-stratification is carried out via a nonparametric regression estimation of the census enumeration and the correct enumeration functions. We propose a nonparametric population size estimator that is designed to accommodate some key aspects of the A.C.E.: missing values, erroneous enumerations, and extra covariates affecting the missingness and correct enumeration. The resulting estimates are compared with estimates from a conventional post-stratification and a logistic regression approach in an analysis on the 2000 Census A.C.E. data. [ABSTRACT FROM AUTHOR]