  We calculate the Boer-Mulders effect contribution to the $\cos2\phi$
azimuthal asymmetry of unpolarized dilepton production near the $Z$-pole. Based
on the tree-level expression in the transverse momentum dependent factorization
framework, we show that the corresponding asymmetry near the $Z$-pole is
negative, which is opposite to the asymmetry in the low $Q^2$ region, dominated
by the production via a virtual photon. We calculate the asymmetry generated by
the Boer-Mulders effect near the $Z$-pole at RHIC, with $\sqrt{s}=500$ GeV. We
find that the magnitude of the asymmetry is several percent, and therefore it
is measurable. The experimental confirmation of this sign change of the
asymmetry from the low $Q^2$ region to the $Z$-pole provides direct evidence of
the chiral odd structure of quarks inside an unpolarized nucleon.
