  We present an analysis of angular distributions and correlations of the
X(3872) particle in the exclusive decay mode X(3872)->J/psi pi+ pi- with
J/psi->mu+ mu-. We use 780 pb -1 of data from ppbar collisions at sqrt{s} =
1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We derive
constraints on spin, parity, and charge conjugation parity of the X(3872)
particle by comparing measured angular distributions of the decay products with
predictions for different JPC hypotheses. The assignments JPC = 1++ and 2-+ are
the only ones consistent with the data.
