Electronic valence- and core-excitations into the anti-bonding orbitals of the H₂S molecule have been calculated within a multi-configurational wave-function framework (RASPT2). Potential energy surfaces and transition dipole moments have been derived in two dimensions for the S-H stretching coordinates. The |S1s^-1, 6a₁¹> and |S1s^-1, 3b₂¹> core-excited states in H₂S are nearly degenerate along the symmetric stretching coordinate, for which we have identified two conical intersections. The small energy splitting of the S1s^-1 core-excited states at equilibrium geometry arise from an avoided crossing at broken symmetry. Compared to the water molecule, which exhibit state-selective gating to different vibrational modes [Nat. Commun. 8 14165 (2017)] in its well-separated O1s^-1 core-excited states, we expect a strong coupling between the close-lying |S1s^-1, 6a₁¹> and |S1s^-1, 3b₂¹> states. This could lead to dissociative dynamics observable in K-edge RIXS. The S2p^-1 core-excited states form two dense manifolds of spin-orbit coupled states, which can be schematically characterised as bound |S2p^-1,3b₂¹> and dissociative |S2p^-1,6a₁¹> states. We identify three conical intersections in the singlet and triplet states along the symmetric stretching coordinate. Mapping the molecular singlet and triplet states to the atomic dissociation limit reveals a symmetry selection rule, leading to an off-set of the ¹|3a₁^-1,6a₁¹> state relative to the other S2p^-1 core-excited states. The dense manifolds of S2p^-1 core-excited states will complicate the analysis of K_α-edge RIXS, but dynamical effects could be evaluated through detuning and in comparison to L-edge XAS. In L-edge RIXS, the dynamical effects well be more pronounced due to a longer life-time of the S2p^-1 core-excited states compared to the S1s^-1 core-excited states.