The transverse target spin azimuthal asymmetry AUTsin(φ-φS) in hard exclusive production of ρ 0 mesons was measured at COMPASS by scattering 160 GeV/c muons off transversely polarised protons and deuterons. The measured asymmetry is sensitive to the nucleon helicity-flip generalised parton distributions E q, which are related to the orbital angular momentum of quarks in the nucleon. The Q 2, x Bj and pT2 dependence of AUTsin(φ-φS) is presented in a wide kinematic range: 1(GeV/c) 2<Q 2<10(GeV/c) 2, 0.003<x Bj<0.3 and 0.05(GeV/c)2<pT2<0.5(GeV/c)2 for protons or 0.10(GeV/c)2<pT2<0.5(GeV/c)2 for deuterons. Results for deuterons are obtained for the first time. The measured asymmetry is small in the whole kinematic range for both protons and deuterons, which is consistent with the theoretical interpretation that contributions from GPDs E u and E d approximately cancel.