We estimate chemical abundances and ionization parameters in the nuclear region of a sample of 143 galaxies from the Palomar Spectroscopic Survey, composed by star-forming galaxies (87), Seyferts 2 (16), and LINERs (40) using the HII-CHI-MISTRY code. We also study for each spectral type the correlation of the derived quantities with other different properties of the host galaxies, such as morphology, stellar mass, luminosity, and mass of their supermassive black holes. The results obtained for star-forming galaxies are used to check the soundness of our methodology. Then, we replicate a similar study for our sample of AGN, distinguishing between Seyferts 2 and LINERs. We report a saturation of Oxygen abundances for the nuclear regions of SFG. The correlations between chemical abundances and their host galaxy properties for SFG are in good agreement with previous studies. We find that Seyferts 2 present slightly higher chemical abundances but this result must be reexamined in larger samples of Seyfert galaxies. In contrast, we obtain lower chemical abundances for LINERs than for SFG. We confirm these relatively lower abundances for another sample of infrared luminous LINERs in the same stellar mass range. Our analysis of AGNs (both LINERs and Seyferts) shows that their host galaxy properties are not correlated with our estimated chemical abundances.