  We present a $^2$D NMR investigation of the gapped spin-1/2 compound $Cu_2
(C_5 H_{12} N_2)_2 Cl_4$. 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 intra-dimer 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.
