  In models with gravitino as the lightest supersymmetric particle(LSP), the
next to lightest supersymmetric particle (NLSP) can have a long lifetime and
appear stable in collider experiments. We study the leptonic signatures of such
a scenario with tau-sneutrino as the NLSP, which is realized in the
non-universal Higgs masses scenario. We focus on an interesting trilepton
signature with two like-sign taus and an electron or a muon of opposite sign.
The neutralinos and charginos are quite heavy in the model considered, and the
trilepton signal comes mostly from the slepton-sneutrino production. We
identify the relevant backgrounds, taking into account tau decays, and devise a
set of cuts to optimize this trilepton signal. We simulate signal and
backgrounds at the LHC with 14 TeV center-of-mass energy. Although the sleptons
in this model are relatively light, O(100 GeV), discovery is more demanding
compared to typical neutralino LSP scenarios. The trilepton signal requires
large amount of accumulated data, at least ~80 fb^-1, at the CM energy of 14
TeV.
