We report on the local electronic structure of interstitial muon (Mu) as pseudo-hydrogen in In-Ga-Zn oxide (IGZO) semiconductor studied by muon spin rotation/relaxation ($mu$SR) experiment. In polycrystalline (c-) IGZO, it is inferred that Mu is in a diamagnetic state, where the $mu$SR time spectra under zero external field is perfectly described by the Gaussian Kubo-Toyabe relaxation function with the linewidth $Delta$ serving as a sensitive measure for the random local fields from In/Ga nuclear magnetic moments. The magnitude of $Delta$ combined with the density functional theory calculations for H (to mimic Mu) suggests that Mu occupies Zn-O bond-center site (Mu$_{rm BC}$) similar to the case in crystalline ZnO. This implies that the diamagnetic state in c-IGZO corresponds to Mu$_{rm BC}^+$, thus serving as an electron donor. In amorphous (a-) IGZO, the local Mu structure in as-deposited films is nearly identical with that in c-IGZO, suggesting Mu$_{rm BC}^+$ for the electronic state. In contrast, the diamagnetic signal in heavily hydrogenated a-IGZO films exhibits the Lorentzian Kubo-Toyabe relaxation, implying that Mu accompanies more inhomogeneous distribution of the neighboring nuclear spins that may involve Mu$^-$H$^-$-complex state in an oxygen vacancy.
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