We investigate the properties and the environment of radio sources with optical counterpart from the combined VLA-COSMOS and zCOSMOS samples. The advantage of this sample is the availability of optical spectroscopic information, high quality redshifts, and accurate density determination. By comparing the star formation rates estimated from the optical spectral energy distribution with those based on the radio luminosity, we divide the radio sources in three families, passive AGN, non-passive AGN and star forming galaxies. These families occupy specific regions of the 8.0-4.5 $μ$m infrared color--specific star formation plane, from which we extract the corresponding control samples. Only the passive AGN have a significantly different environment distribution from their control sample. The fraction of radio-loud passive AGN increases from ~2% in underdense regions to ~15% for overdensities (1+delta) greater than 10. This trend is also present as a function of richness of the groups hosting the radio sources. Passive AGN in overdensities tend to have higher radio luminosities than those in lower density environments. Since the black hole mass distribution is similar in both environments, we speculate that, for low radio luminosities, the radio emission is controlled (through fuel disponibility or confinement of radio jet by local gas pressure) by the interstellar medium of the host galaxy, while in other cases it is determined by the structure (group or cluster) in which the galaxy resides. Comment: 17 pages, 17 figures, A&A in press