Altmetrics promise useful support for assessing the impact of scientific works, including beyond the scholarly community and with very limited citation windows. Unfortunately, altmetrics scores are currently available only for recent articles and cannot be used as covariates in predicting long term impact of publications. However, the study of their statistical properties is a subject of evident interest to scientometricians. Applying the same approaches used in the literature to assess the universality of citation distributions, the intention here is to test whether the universal distribution also holds for Mendeley readerships. Results of the analysis carried out on a sample of publications randomly extracted from the Web of Science confirm that readerships seem to share similar shapes across fields and can be rescaled to a common and universal form. Such rescaling results as not particularly effective on the right tails. In other regions, rescaling causes a good collapse of field specific distributions, even for very recent publications.