We present near-infrared (NIR) spectroscopic observations of 28 X-ray and mid-infrared selected sources at a median redshift of z ˜ 0.8 in the Extended Groth Strip (EGS). To date this is the largest compilation of NIR spectra of active galactic nuclei (AGN) at this redshift. The data were obtained using the multi-object spectroscopic mode of the Long-slit Intermediate Resolution Infrared Spectrograph (LIRIS) at the 4.2 m William Herschel Telescope (WHT). These galaxies are representative of a larger sample studied in a previous work, consisting of over a hundred X-ray selected sources with mid-infrared counterparts, which were classified either as AGN dominated or host galaxy dominated, depending on the shape of their spectral energy distributions (SEDs). Here, we present new NIR spectra of 13 and 15 sources of each class, respectively. We detect the Hα line at ≥1.5σ above the continuum for the majority of the galaxies. Using attenuation-corrected Hα luminosities and observed Spitzer/MIPS 24 μm fluxes, and after subtracting an AGN component estimated using an AGN empirical correlation and multifrequency SED fits, we obtain average star formation rates (SFRs) of 7 ± 7 and 20 ± 50 M&sun; yr-1, respectively (median SFRs = 7 and 5 M&sun; yr-1). These values are lower than the SFRs reported in the literature for different samples of non-active star-forming galaxies of similar stellar masses and redshifts (M* ˜ 1011 M&sun; and z ˜ 1). In spite of the small size of the sample studied here, as well as the uncertainty affecting the AGN-corrected SFRs, we speculate with the possibility of AGN quenching the star formation in galaxies at z ˜ 0.8. Alternatively, we might be seeing a delay between the offset of the star formation and AGN activity, as observed in the local Universe.