The production of J/ψ's resulting from ultrarelativistic nucleus-nucleus collisions is described by the semi-local duality model. The J/ψ production rate is studied in Bjorken's (1 + 1)-dimensional scaling expansion system. Its correlation with the secondary-hadron multiplicity is analyzed in detail. Furthermore, the J/ψ suppression caused by the deconfinement and absorption mechanisms is examined and their effects on this correlation are analyzed once again. In the plots of this correlation only a plateau remains in the case of the J/ψ suppression and this character could be used as a signal for diagnosing the mixed phase of QCD matter.