We report on the properties of SrTb₂O₄, a frustrated zigzag ladder antiferromagnet, studied by single crystal neutron diffraction (with polarized neutrons in zero field and unpolarized neutrons in an applied magnetic field), as well as by neutron spectroscopy on a polycrystalline sample. The neutron scattering results are supported by single-crystal magnetization and heat capacity measurements. In zero field, neutron diffraction data show no transition to a magnetically ordered state down to the lowest experimentally available temperature of 35 mK, and the material remains magnetically disordered down to this temperature. Polarized neutron diffraction measurements reveal the presence of a diffuse scattering signal suggesting only very weak spin-spin correlations in the ground state. For H c (the easy magnetization direction), we followed the magnetization process using neutron diffraction measurements and observed the appearance of field-induced magnetic Bragg peaks with integer h and k indices in the (hk0) scattering plane. No magnetic peaks with a nonzero propagation vector were detected. The observed in-field data fit well to a simple two-sublattice model with magnetic moments aligned along the field direction but being significantly different in magnitude for the two inequivalent Tb³⁺ sites in the unit cell. Overall, the collected data point to a nonmagnetic ground state in SrTb₂O₄ despite the presence of strong interactions.