This thesis presents preliminary results of a search for Higgs boson production in association with top quarks in multilepton final states. The search was conducted in the 2012 dataset of proton-proton collisions delivered by the CERN Large Hadron Collider at a center-of-mass energy of 8 TeV and collected by the ATLAS experiment. The dataset corresponds to an integrated luminosity of 20.3 inverse femtobarns. The analysis is conducted by measuring event counts in signal regions distinguished by the number of leptons (2 same-sign, 3, and 4), jets and b-tagged jets present in the reconstructed events. The observed events in the signal regions constitute an excess over the expected number of background events. The results are evaluated using a frequentist statistical model. The observed exclusion upper limit at the 95 % confidence level is 5.50 times the predicted Standard Model production cross section for Higgs production in association with top quarks. The fitted value of the ratio of the observed production rate to the expected Standard Model production rate is 2.83 $+$ 1.58 $-$ 1.35.