In this paper we study the nuclear obscuration of galaxies hosting LINERs based on their X-ray and optical emission. They show column densities (N_H) at soft energies (0.5-2 keV) mostly related to the diffuse emission around the AGN, showing a correlation with the optical extinction. N_H at hard energies (2-10 keV) seem to be much higher than what would be expected from the optical extinction. They might be associated to the inner regions of the AGN, buried at optical wavelengths. The main result of this paper is that around 50% of our LINER sample shows signatures of Compton-thickness (CT) according to the most common tracers: the X-ray spectral index, F(2-10 keV)/F([OIII]) ratio and EW(FeKa). However, the EWs of CT LINERs are significantly lower than in CT Sy, suggesting that the 2-10 keV emission is dominated by electron scattering of the otherwise invisible AGN, or by emission from shocked gas associated to star formation rather than by reflection from the inner wall of the torus. However, no clear relation seems to exist between galaxies with optical dust lanes and X-ray classified CT objects. This may suggest that CT sources should be related to absorbing material located at the very inner regions of the AGN, maybe in the putative dusty torus. Larger M_BH and lower Eddington ratios than Sy galaxies have been found. This effect can be better attributed to LINER nuclei being hosted by earlier morphological types than Sy nuclei. However, it has to be noted that, once a proper correction to the X-ray luminosity is applied, LINERs show Eddington ratios overlapping those of Sy 2. We speculate with a possible scenario for LINER nuclei: an inner obscuring matter similar to that of Sy 2, and an external obscuring matter responsible for the optical extinction. CT sources appear to be more common among LINERs than Sy.

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