Here, we present experimental evidence of the pseudodoublet ground state of the non-Kramers compound SrTm₂⁢O₄, based on specific heat, magnetic entropy, and electron paramagnetic resonance. We demonstrate that the two crystallographic Tm³⁺ sites give rise to distinct single-ion anisotropies, and by extension, SrTm₂⁢O₄ hosts two magnetic sublattices. Inelastic neutron scattering reveals low-lying dispersing crystal-field excitations, which we modeled using an effective charge model and mean-field random phase approximation. The extracted magnetic exchange interactions are both antiferromagnetic and frustrated for both sublattices. The magnetic exchange interactions between the different sublattices are negligible. The strength of the magnetic exchange interactions in relation to the size of the crystal-field energy gaps, together with the frustration and low dimensionality, force the system to remain paramagnetic down to the lowest experimentally reachable temperature despite the pseudodoublet nature of its ground state.