The crystal structure if RbH₂PO₄ has been determined by neutron diffraction at room temperature and T_c+5K in the tetragonal (paraelectric) phase using single-crystal samples. The techniques of constrained refinement and statistical testing have been used to examine carefully the significance of some pertinent structural features. The crystal structure has also been determined at 77K in the orthorhombic (ferroelectric) phase using neutron powder-diffraction methods. The results for both phases are compared with those obtained from similar studies of KH₂PO₄. Whilst it is shown that the crystal structures of RbH₂PO₄ and KH₂PO₄ (and the way they change through the transition) are closely similar, some small but important differences are revealed. In particular, the separation of the 'disordered' proton sites in the tetragonal phase is significantly larger in RbH₂PO₄ (by approximately 0.05 AA); yet the hydrogen-bond lengths differ by only 0.003(2) AA, and the transition temperatures by only approximately 20K.