A search for the associated production of the Higgs boson with a top quark pair is performed in multilepton final states using 20.3 fb-1 of proton-proton collision data recorded by the ATLAS experiment at s=8 TeV at the Large Hadron Collider. Five final states, targeting the decays H→WW*, ττ, and ZZ*, are examined for the presence of the Standard Model (SM) Higgs boson: two same-charge light leptons (e or μ) without a hadronically decaying τ lepton; three light leptons; two same-charge light leptons with a hadronically decaying τ lepton; four light leptons; and one light lepton and two hadronically decaying τ leptons. No significant excess of events is observed above the background expectation. The best fit for the tt-H production cross section, assuming a Higgs boson mass of 125 GeV, is 2.1-1.2+1.4 times the SM expectation, and the observed (expected) upper limit at the 95% confidence level is 4.7 (2.4) times the SM rate. The p-value for compatibility with the background-only hypothesis is 1.8σ the expectation in the presence of a Standard Model signal is 0.9σ.