We propose a method to identify the source and target regions of a copy-move forgery so allow a correct localisation of the tampered area. First, we cast the problem into a hypothesis testing framework whose goal is to decide which region between the two nearly-duplicate regions detected by a generic copy-move detector is the original one. Then we design a multi-branch CNN architecture that solves the hypothesis testing problem by learning a set of features capable to reveal the presence of interpolation artefacts and boundary inconsistencies in the copy-moved area. The proposed architecture, trained on a synthetic dataset explicitly built for this purpose, achieves good results on copy-move forgeries from both synthetic and realistic datasets. Based on our tests, the proposed disambiguation method can reliably reveal the target region even in realistic cases where an approximate version of the copy-move localization mask is provided by a state-of-the-art copy-move detection algorithm.