We investigate the X-ray properties of BzK-selected galaxies at z~2 using deep X-ray data in the Chandra Deep Field-South (CDFS) and Chandra Deep Field-North (CDFN). A subset of these BzK galaxies have been proposed as Compton-thick active galactic nucleus (AGN) candidates based on a high ratio of infrared (IR) to ultraviolet (UV) star formation rates (SFRs). With the benefit of deep 24{mu}m observations, our sample of these IR-excess galaxies is larger than previous studies and combined with the deepest X-ray data yield new insights into the population. We identify 701 and 534 star-forming BzK galaxies (sBzK galaxies) in the range z=1.2-3.0 in CDFS and CDFN, respectively. Of these we directly detect in X-rays 49 sBzK galaxies in CDFS and 32 sBzK galaxies in CDFN.