We investigate signs of Active Galactic Nucleus (AGN) in the luminous infrared galaxy NGC 3256 at both infrared and X-ray wavelengths. NGC 3256 has double, the Northern and Southern, nuclei (hereafter, N and S nuclei, respectively). We show that the Spitzer IRAC colors extracted at the S nucleus are AGN-like, and the Spitzer IRS spectrum is bluer at <6um than at the N nucleus. We built for the S nucleus an AGN-starburst composite model with a heavily absorbed AGN to successfully reproduce not only the IRAC and IRS specrophotometries at ~3arcsec but also the very deep silicate 9.7um absorption observed at 0.36 scale by Diaz-Santos et al. We found a 2.2um compact source at the S nucleus in a HST NICMOS image and identified its unresolved core (at 0.26 resolution) with the compact core in previous mid-infrared observations at comparable resolution. The flux of the 2.2umm core is consistent with our AGN spectral energy distribution model. We also analyzed a deeper than ever Chandra X-ray spectrum of the unresolved (at 0.5 resolution) source at the S nucleus. We found that a dual-component power-law model (for primary and scattered ones) fits an apparently very hard spectrum with a moderately large absorption on the primary component. Together with a limit on equivalent width of a fluorescent Fe-K emission line at 6.4 keV, the X-ray spectrum is consistent with a typical Compton-thin Seyfert 2. We therefore suggest that the S nucleus hosts a heavily absorbed low-luminosity AGN.