Yields for J/psi production in Cu+Cu collisions at sqrt s_NN=200 GeV have been measured over the rapidity range |y|<2.2 and compared with results in p+p and Au+Au collisions at the same energy. The Cu+Cu data offer greatly improved precision over existing Au+Au data for J/psi production in collisions with small to intermediate numbers of participants, in the range where the quark-gluon plasma transition threshold is predicted to lie. Cold nuclear matter estimates based on ad hoc fits to d+Au data describe the Cu+Cu data up to N_part approximately 50, corresponding to a Bjorken energy density of at least 1.5 GeV/fm(3).