The first search for a narrow, high-mass resonance decaying into Z and Higgs (H) bosons is presented. The final state studied consists of a merged jet pair and a $\tau$ pair resulting from the decays of Z and H bosons, respectively. The analysis is based on a data sample of proton-proton collisions at a center-of-mass energy of 8 TeV, collected with the CMS experiment in 2012, and corresponding to an integrated luminosity of 19.7 fb$^{-1}$. In the resonance mass range of interest, the Z and H bosons are produced with large momenta, which implies that the final products of the two quarks or the two $\tau$ leptons must be detected within a small angular interval. From a combination of all possible decay modes of the $\tau$ leptons, production cross sections in a range between 0.9 and 27.8 fb are excluded at 95% confidence level, depending on the resonance mass.

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