Abstract: In this thesis a search for a CP-odd Higgs boson A decaying into a Z boson and a neutral CP-even Higgs boson h with a mass of 125 GeV is described. The search is based on proton-proton collision data at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in the years 2015 and 2016 corresponding to an integrated luminosity of 36/fb. Final states, where the Z boson decays into pairs of electrons, muons or neutrinos and the h boson into bottom-quark pairs, are considered. The presence of neutrinos is inferred by a momentum imbalance in the transverse plane, the bottom-quark pairs are reconstructed either as two small-radius or one large-radius calorimeter jet(s). The reconstructed invariant or transverse mass distributions of the Zh candidates are searched for the presence of localised excesses above the expectation from known Standard Model processes. No evidence for an A-boson signal is found. Upper limits on the A-boson production cross-section times the branching fractions for A-boson decays into Zh and h-boson decays to bottom-quark pairs are derived at the 95% confidence level for A bosons with masses between 220 GeV and 2 TeV; they range between 0.0019 pb and 0.81 pb. The results are interpreted in the context of Two-Higgs-Doublet Models. Furthermore, a novel method to calibrate the b-tagging efficiency for c-quark jets is described. It is demonstrated for the standard b-tagging algorithm of the ATLAS experiment in Run 1 using proton-proton collision data at a centre-of-mass energy of 7 TeV collected with the ATLAS detector in the year 2011. The calibration uses a sample of c jets obtained from events, where a W boson is produced in association with a single c quark; the resulting c jet is identified by a muon stemming from the semileptonic c-hadron decay. The measured c-jet tagging efficiencies are presented relative to the corresponding efficiencies in simulated W+c events as scale factors. The measured scale factors are extrapolated using a simulation-based and data-supported procedure to obtain scale factors valid for inclusive samples of c jets. Their uncertainties range between 5% and 13 %.