We investigate the pattern of asymmetries in the color-octet model for
inclusive production of charmonium with polarized initial state hadro
ns and photons. The double polarized asymmetry for J/psi involves a ne
w combination of long-distance matrix elements. We also investigate th
e asymmetries for eta(c), chi(c), and Y production. The asymmetries di
stinguish well between different models of charmonium production.