In this paper, we consider the inverse problem of estimating the product f g of two densities, given a n-sample of i.i.d. observations drawn from each. We propose both projection estimators with model selection device and kernel estimators with bandwidth selection strategies. The procedures do not consist in making the product of each density estimator, but in plugging an overfitted estimator of one of the two densities, in an estimator based on the second sample. Our findings are a first step toward a better understanding of the good performances of overfitting in regression Nadaraya-Watson estimator.