A search for the production of two Higgs bosons decaying to bZZ is presented. The analysis is based on data collected by the CMS detector during the 2016 proton-proton running of the LHC, corresponding to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. The bZZ final states considered are the ones where one Z decays leptonically into two oppositely charged leptons (either two muons or two electrons), and the other Z decays either to two neutrinos or hadronically into two or more jets. Upper limits at confidence level are placed on the production of a narrow-width spin-0 or spin-2 particle decaying to a pair of Higgs bosons. This is the first search for Higgs boson resonant pair production in the final state where the other Z boson decays hadronically into two or more jets.