Sum-Product Networks (SPN) are deep probabilistic models that have shown to achieve state-of-the-art performance in several machine learning tasks. As with many other probabilistic models, performing Maximum-A-Posteriori (MAP) inference is NP-hard in SPNs. A notable exception is selective SPNs, that constrain the network so as to allow MAP inference to be performed in linear time. Due to the high number of parameters, SPNs learned from data can produce unreliable and overconfident inference; this phenomenon can be partially mitigated by performing a Robustness Analysis of the model predictions to changes in the parameters. In this work, we address the problem of assessing the robustness of MAP inferences produced with Selective SPNs to global perturbations of the parameters. We present efficient algorithms and an empirical analysis with realistic problems.