We present a 2D NMR investigation of the gapped spin-1/2 compound Cu2(C5H10N2D2)2Cl4. Our measurements reveal the presence of a magnetic field-induced transverse staggered magnetization (TSM) which persists well below and above the field-induced 3D long-range magnetically ordered (FIMO) phase. The symmetry of this TSM is different from that of the TSM induced by the order parameter of the FIMO phase. Its origin, field dependence, and symmetry can be explained by an intradimer Dzyaloshinskii-Moriya interaction, as shown by DMRG calculations on a spin-1/2 ladder. This leads us to predict that the transition into the FIMO phase is not in the BEC universality class.