Platinum(II) complexes exhibiting an expressed dz2-nucleophilicity of the positively charged metal centers, namely, [Pt(ppy)(acac)] (1; acacH is acetylacetone; ppyH is 2-Ph-pyridine) and [Pt(ppy)(tmhd)] (2; tmhdH is 2,2,6,6-tetramethylheptanedione-3,5), were cocrystallized with the chalcogen bond donors (4-NC5F4)2Ch (Ch = Se, Te) to form two isostructural cocrystals 1·1/2(4-NC5F4)2Ch, and 2·2/3(4-NC5F4)2Se and 2·(4-NC5F4)2Te. The X-ray data for these cocrystals and appropriate theoretical DFT calculations (PBE0-D3BJ) allowed the recognition of the metal-involving chalcogen bond, namely, Ch···dz2-PtII (its energy spans from -7 to -12 kcal/mol). In 1·1/2(4-NC5F4)2Ch, Ch···dz2-PtII bonding is accompanied by the C···dz2-PtII interaction, representing a three-center bifurcate, whereas in 2·(4-NC5F4)2Te the chalcogen bond Te···dz2-PtII is purely two-centered and is stronger than that in 1·1/2(4-NC5F4)2Ch because of more efficient orbital overlap. The association of 2 with (4-NC5F4)2Te and the structure of the formed adduct in CDCl3 solutions was studied by using 1H, 13C, 19F, 195Pt, 125Te NMR, 19F-1H HOESY, and diffusion NMR methods. The 195Pt and 125Te NMR titration and the isothermal titration calorimetry results revealed a 1:1 association of 2 with (4-NC5F4)2Te.