A search for $B^{0}_{s}totau^{pm}mu^{mp}$ and $B^{0}totau^{pm}mu^{mp}$ decays is performed using data corresponding to an integrated luminosity of 3 fb$^{-1}$ of proton-proton collisions, recorded with the LHCb detector in 2011 and 2012. For this search, the $tau$ lepton is reconstructed in the $tau^{-}topi^{-}pi^{+}pi^{-} u_{tau}$ channel. No significant signal is observed. Assuming no contribution from $B^{0}totau^{pm}mu^{mp}$ decays, an upper limit is set on the $B^{0}_{s}totau^{pm}mu^{mp}$ branching fraction of $mathcal{B}left( B^{0}_{s}totau^{pm}mu^{mp}right) < 4.2times 10^{-5}$ at $95%$ confidence level. If instead no contribution from $B^{0}_{s}totau^{pm}mu^{mp}$ decays is assumed, a limit of $mathcal{B}left( B^{0}totau^{pm}mu^{mp}right) < 1.4times 10^{-5}$ is obtained at $95%$ confidence level. These are the first limit on $mathcal{B}left( B^{0}_{s}totau^{pm}mu^{mp}right)$ and the worlds best limit on $mathcal{B}left( B^{0}totau^{pm}mu^{mp}right)$.
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