We analyze the implications of CP-violating scalar leptoquark (LQ) interactions for experimental probes of parity- and time-reversal violating properties of polar molecules. These systems are predominantly sensitive to the electric dipole moment (EDM) of the electron and nuclear-spin-independent (NSID) electron-nucleon interaction. The LQ model can generate both a tree-level NSID interaction as well as the electron EDM at one-loop order. Including both interactions, we find that the NSID interaction can dominate the molecular response. For moderate values of couplings, the current experimental results give roughly two orders of magnitude stronger limits on the electron EDM than one would otherwise infer from a sole-source analysis.