The pure rotational spectra of seven isotopic species of platinum monoxide have been measured with a cavity pulsed jet Fourier-transform microwave spectrometer. The molecules were prepared by laser ablation of Pt foil in the presence of O2 and stabilized in a supersonic jet of argon. A multi-isotopomer Dunham-type analysis of the spectra produced values for Y01 and Y11, along with unusually large values for Born-Oppenheimer breakdown (BOB) parameters for both Pt and O atoms. The values of the BOB parameters have been rationalized in terms of the molecular electronic structure and finite nuclear size (field shift) effects. A large negative 195Pt effective nuclear spin-rotation constant has been rationalized in terms of the electron-nucleus dipole-dipole hyperfine constant. Precise internuclear separations have been evaluated.