Two new palladium (II) complexes, [Pd (phen)(pip-dtc)]$NO_3$ and [Pd(phen)(mor-dtc)]$NO_3$, (where phen is 1,10-Phenantroline, pip-dtc is piperidinedithiocarbamate anion and mor-dtc is morpholinedithiocarbamate anion) have been synthesized and characterized by elemental analysis, spectroscopic studies (FT-IR, $^1H$ NMR, UV-Vis) and conductance measurement. In these complexes, the dithiocarbamate ligands coordinate with Pd (II) center as bidentate with two sulfur atoms. These two complexes have been tested against chronic myelogenous leukemia cell line, K562. They show $IC_{50}$ values less than cisplatin and thus the mode of binding of the complexes to calf thymus DNA (CT-DNA) were investigated by ultraviolet difference and fluorescence spectroscopy. They can denature DNA, exhibit cooperative binding and intercalate into DNA. Several binding and thermodynamic parameters are also described.