Direct searches for lepton flavor violating Higgs boson decays in the τ μ channel have been recently reported by the CMS collaboration. The results display a slight excess of signal events with a significance of 2.5σ, which translates into a branching ratio of about 1%. By interpreting these findings as a hint for beyond the standard model physics, we show that the Type-III 2HDM is capable of reproducing such signal while at the same time satisfying vacuum stability, perturbativity, electroweak precision data, measured Higgs standard decay modes and low-energy lepton flavor violating constraints. We have found that the allowed signal strength ranges for the bb, WW* and ZZ* standard channels shrink as soon as BR(h→τμ)∼ 1% is enforced. Thus, we point out that if the excess persists, improved measurements of these channels may be used to test our Type-III 2HDM scenario.