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A search for Bs → τ+μ- and B0 → τ+μ- decays is performed using data corresponding to an integrated luminosity of 3 fb−1 of proton–proton collisions recorded by the LHCb experiment during 2011 and 2012. For this search, the τ lepton is reconstructed in the 3-prong τ+→ π+ π+π- ν channel. The full event selection is presented and a fit strategy is proposed to extract the signal yields. Using the B0 → D+(→ K- π+ π+)π normalization mode, the yields are turned into branching ratios or, in the absence of signals, into limits on the branching ratios.