We study the phenomenological implications of interference between tree-level contributions to decays to three-body final states. CP-violation in these decays arise via different virtualities of intermediate resonances, and the presence of SM and/or new CP phases in a model Lagrangian. We highlight the manifestation of this CP-violating observable in the interference between SM charged-current decays and new-physics contributions to effective vector interactions in the EFT and in a UV-complete model featuring a scalar leptoquark, $S_1$. We present a novel method for searching for CP-violating new physics effects utilising the differential cross sections of $pp\to d_i \ell\nu_\ell$ decays, with a detailed study of $pp\to b \tau\nu_\tau$ simulating signal and background.