The inability of the standard model (SM) to explain some observed phenomena motivates theoretical models featuring an extension of the SM scalar sector that predict additional Higgs bosons. The Two-Higgs-doublet model (2HDM) is one of these. This note reports on a search for an extended scalar sector, where a new CP-even (odd) boson decays to a Z boson and a lighter CP-odd (even) boson, which further decays to $\mathrm{b}\overline{\mathrm{b}}$. The Z boson is reconstructed via its decays to leptons. The analysed data were recorded in proton-proton collisions at $\sqrt{s} = 13$ TeV, collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Data and predictions from the SM are in agreement within uncertainties. Upper limits at 95% confidence level are set on the signal production cross section times branching fraction, with masses of the resonances ranging up to 1000 GeV. The results are interpreted in the context of the Type-II 2HDM.