Virtually all data collection efforts experience item nonresponse. A common approach to account for item nonresponse is to perform imputation using a series of generalized regression models. Typically, these models are fit to the observed data using only main effects, and donor values are drawn from the posterior distributions of the variables needing imputation. Unfortunately, this "prediction model" approach does not consider the probabilities of item response. Evidence suggests that using both a prediction model and a response propensity model in imputation can yield estimates with smaller mean squared error. I propose a nonparametric imputation method that uses both a tree-based prediction model, a tree-based response propensity model, and approximate Bayesian bootstrap. Note that the double-robustness implies that only one of the tree-based models needs to be correct. Using simulated data, a Monte Carlo simulation demonstrates that my proposed method performs as well or better than a series of generalized linear models using main effects.