We study charged lepton flavor violating Higgs boson decay process in the gauged two Higgs doublet model. The model introduces an additional SU(2)H gauged symmetry and combines two Higgs doublet H1 and H2 into a SU(2)H doublet H. We examine the neutrino mass mechanisms, including Dirac Type and Majorana type. In the latter, neutrino mass is achieved by the type-II seesaw mechanism with an additional SU(2)H triplet
∆N . ∆N is included here in the scalar potential and scalar mass spectrum. We present six Feynman diagrams of charged lepton flavor violating Higgs decay and calculate two
classic diagrams among them. It is shown W0 exchanging diagrams are the largest and we discuss how the amplitude will be determined by various parameters. In typical situation
the branching ratio is in the order around 10^−10 or smaller, probably beyond the ability of the Large Hadron Collider measurements to detect. However in some extreme case of
parameters, especially large Yukawa couplings, the branching ratio could be as large as 10^−6 and the H± exchanging diagrams could become more important.

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