Hydrogen absorption of the CeFeSi- and CeScSi-type forms of GdTiGe was performed. Before hydrogenation they show an antiferromagnetic transition at around 412 K and a ferromagnetic transition at 376 K, respectively. Hydrogenation of both forms leads to formation of the same hydride GdTiGeH which crystallizes with a filled CeScSi-type structure where all the [Gd-4] tetrahedra are filled by hydrogen. This hydride is paramagnetic in the temperature range 4-300 K. The slightly negative value of the paramagnetic Curie temperature theta(p) confirms that all ferromagnetic interactions were destroyed in the case of the CeScSi-type form. From first-principles calculations with the PAW GGA methodology, the localization of hydrogen within the [Gd-4] tetrahedra was confirmed through energetic stabilization. It was also seen that the energy changes significantly with volume, indicating the itinerant (delocalized) role of the electrons in the magnetism.