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 boundedness from below of the scalar potential, 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, W W * and ZZ * standard channels shrink as soon as BR(h → τ µ) ∼ 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.