This paper introduces a two-dimensional Item Response Theory (IRT) model to deal with nonignorable nonresponses in tests with dichotomous items. One dimension provides information about the omitting behavior, while the other dimension is related to the person’s “ability”. The idea of embedding an IRT model for missingness into the measurement model is not new but, differently from the existing literature, the model presented in this paper belongs to the Rasch family of models. As a member of the exponential family, the model offers several advantages, such as existence of non trivial sufficient statistics and possibility of specific objective parameter estimation; feasibility of conditional inference; goodness of fit analysis via conditional likelihood ratio tests. Maximum likelihood estimation is discussed, and the applicability of the proposed model is illustrated by using a real data set.