We present near-infrared (NIR) spectroscopic observations of 28 X-ray and mid-infrared 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 AGN are representative of a larger sample studied in a previous work, consisting of over a hundred X-ray selected AGN with mid-infrared counterparts, which were classified either as AGN-dominated or host galaxy-dominated (i.e. buried AGN) 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 ≥ 1.5 σ above the continuum for the majority of the galaxies. Using attenuation-corrected Hα luminosities, and after subtracting an AGN component that we estimate using an AGN empirical correlation, we obtain a median star formation rate (SFR) of 7±7 {M}_{&sun;} year^{-1}. This SFR is lower than those reported in the literature for different samples of non-active star-forming galaxies of similar stellar masses and redshifts (M_*˜ 10^{11} {M}_&sun; and z˜1). Despite the small size of the sample, we speculate on 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 the AGN activity, as observed in the local Universe.