The NA60 experiment collected data on dimuon production in indium-indium collisions at 158 GeV/c per incident nucleon, in year 2003, to contribute to the clarification of several questions raised by previous experiments studying high-energy heavy-ion physics at the CERN SPS in search of the quark gluon plasma. Among these previous results stands the observation, by NA50, that the production yield of J/ψ mesons is suppressed in central Pb-Pb collisions beyond the normal nuclear absorption defined by proton-nucleus data. By comparing the centrality dependence of the suppression pattern between different colliding systems, S-U, Pb-Pb and In-In, we should be able to identify the corresponding scaling variable, and the physics mechanism driving the suppression. In this paper, we will present the ratio of J/ψ and Drell-Yan production cross-sections in indium-indium collisions, in three centrality bins, and how these values compare to previous measurements. We will also present a study of the transverse momentum distributions of the J/ψ mesons, in seven centrality bins.