We discuss the X-ray properties of the radio sources detected in a deep 1.4 and 5 GHz VLA Radio survey of the Extended Chandra Deep Field South (E-CDFS). Among the 266 radio sources detected, we find 89 sources (1/3 of the total) with X-ray counterparts in the catalog of the 1Ms exposure of the central 0.08 deg^2 (Giacconi et al. 2002; Alexander et al. 2003) or in the catalog of the 250 ks exposure of the 0.3 deg^2 E-CDFS field (Lehmer et al. 2005). For 76 (85%) of these sources we have spectroscopic or photometric redshifts, and therefore we are able to derive their intrinsic properties from X-ray spectral analysis, namely intrinsic absorption and total X-ray luminosities. We find that the population of submillijansky radio sources with X-ray counterparts is composed of a mix of roughly 1/3 star forming galaxies and 2/3 AGN. The distribution of intrinsic absorption among X-ray detected radio sources is different from that of the X-ray selected sample. Namely, the fraction of low absorption sources is at least two times larger than that of X-ray selected sources in the CDFS. This is mostly due to the larger fraction of star forming galaxies present among the X-ray detected radio sources. If we investigate the distribution of intrinsic absorption among sources with L_X>10^42 erg s^-1 in the hard 2-10 keV band (therefore in the AGN luminosity regime), we find agreement between the X-ray population with and without radio emission. In general, radio detected X-ray AGN are not more heavily obscured than the non radio detected AGN. This argues against the use of radio surveys as an efficient way to search for the missing population of strongly absorbed AGN.