A conical intersection exists between the ground (1 (2) A') and the first-excited (2 (2)A') electronic potential energy surfaces (PESs) of the H-3 system for C-3 upsilon geometries. This intersection induces a geometric phase effect, an important factor in accurate quantum mechanical reactive scattering calculations, which at low energies can be performed using the ground PES only, together with appropriate nuclear motion boundary conditions. At higher energies, however, such calculations require the inclusion of both the 1 (2)A' and 2 (2)A' electronic PESs and the corresponding nuclear derivative couplings. Here we present ab initio first-derivative couplings for these states obtained by analytic gradient techniques and a fit to these results. We also present a fit to the corresponding 1 (2)A' and 2 (2)A' adiabatic electronic PESs, obtained from the ab initio electronic energies. The first-derivative couplings are compared with their approximate analytical counterparts obtained by Varandas [J. Chem. Phys. 86, 6258 (1987)] using the double many-body expansion method. As expected, the latter are accurate close to conical intersection configurations but not elsewhere. We also present the contour integrals of the ab initio couplings along closed loops around the above-mentioned conical intersection, which contain information about possible interactions between the 2 (2)A' and 3 (2)A' states.