  Frequency shifts and nuclear relaxations of 13C NMR of the metal-insulator
alternating material, (Me-3,5-DIP)[Ni(dmit)2]2, are presented. The NMR
absorption lines originating from metallic and insulating layers are well
resolved, which evidences the coexistence of localized spins (\pi_loc) and
conduction \pi-electrons. The insulating layer is newly found to undergo
antiferromagnetic long range order at about 2.5 K, suggesting emergence of
S=1/2 Mott insulator. In the metallic layer, we found significant suppressions
of static and dynamical susceptibilities of conduction electrons below 35 K,
where antiferromagnetic correlation in the insulating layer evolves. We propose
a dynamical effect through strong \pi-\pi_loc coupling between the metallic and
insulating layers as an origin of the reduction of the density of states.
