A measurement of $Zrightarrowtau^+tau^-$ production cross-section is presented using data, corresponding to an integrated luminosity of 2 fb$^{-1}$, from $pp$ collisions at $sqrt{s}=8$ TeV collected by the LHCb experiment. The $tau^+tau^-$ candidates are reconstructed in final states with the first tau lepton decaying leptonically, and the second decaying either leptonically or to one or three charged hadrons. The production cross-section is measured for $Z$ bosons with invariant mass between 60 and 120 GeV/$c^2$, which decay to tau leptons with transverse momenta greater than 20 GeV/$c$ and pseudorapidities between 2.0 and 4.5. The cross-section is determined to be $sigma_{pprightarrow{}Zrightarrow{}tau^+tau^-} = 95.8 pm 2.1 pm 4.6 pm 0.2 pm 1.1 mathrm{pb}$, where the first uncertainty is statistical, the second is systematic, the third is due to the LHC beam energy uncertainty, and the fourth to the integrated luminosity uncertainty. This result is compatible with NNLO Standard model predictions. The ratio of the cross-sections for $Zrightarrowtau^+tau^-$ to $Zrightarrowmu^+mu^-$ ($Zrightarrow{}e^+e^-$), determined to be $1.01 pm 0.05$ ($1.02 pm 0.06$), is consistent with the lepton-universality hypothesis in $Z$ decays.
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