We discuss criteria for placing a selection cut on the output of a neural network used for event selection. Two such criteria are postulated. One of these, namely the criterion of optimal combined error resulting from the statistics of the signal and the background, is analyzed. This is illustrated for the simple case of a quantity, such as cross-section, which is linearly dependent on the number of events. The existence of optimized solution(s) may be analyzed on the efficiencypurity plot, on which a neural network selector is a single valued curve.