We have investigated effects of surface hydrogenation on the topological properties of multilayer graphene by using density functional theory calculations and a tight-binding model. Hydrogen adsorption on a dimer site of a surface layer decouples the surface layer from the rest of the layers. Hydrogen adsorption on a nondimer site introduces a band mixing between the hydrogenated graphene and the rest of the graphene layers. The valley Hall effects and spin-valley-resolved Chern numbers of multilayer graphene, calculated as a function of the sublattice potential and the potential perpendicular to the layers, was found to be sensitive to details of inversion symmetry-breaking potentials. While the topological invariant depends on the adsorption site and spin polarization, surface-hydrogenated M-layer graphene was found to be topologically equivalent to (M-1)-layer graphene under inversion symmetry-breaking potentials regardless of the adsorption site.