In supersymmetric models with nonzero Majorana neutrino mass, the sneutrino and antisneutrino mix, which may lead to same-sign dilepton signals in future collider experiments. We point out that the anomaly-mediated supersymmetry breaking scenario has a good potential to provide an observable rate of such signals for the neutrino masses suggested by the atmospheric and solar neutrino oscillations. It is noted also that the sneutrino-antisneutrino mixing can provide much stronger information on some combinations of the neutrino masses and mixing angles than the neutrino experiments.