The decay of 2.6 min 64Ga produced by the reaction 64Zn(p, n) 64Ga has been studied by Ge(Li) γ-ray spectroscopy, NaI(TI) crystals both singly and in coincidence, and β-γ(CP) correlation measurements. A transmission type of polarimeter was used in the correlation measurements to give good discrimination against lower energy γ-rays. The decay was found to populate excited states in 64Zn at 991.3, 1799.2, 1909.8, 2608.5, 3186.2, 3261.7, 3365.9 3425.0, 3795.0, 4453.5 keV, and possibly 3623 keV. The decay properties of these states were generally found to agree well with the (p, p'γ) work of Van Patter and co-workers. Beta-gamma (CP) correlation measurements were made on β rays in coincidence with strong ground state γ-ray transitions from the states at 3365.9 and 3425.0 keV. The combined asymmetry parameter of -1.00±0.05 strongly favours a spin of 0 for the 64Ga ground state; a spin of 1 would be possible only if the mixing into the 64Ga ground state involves a very large Coulomb matrix element of ⪸ 344 keV. Possible explanations of the unusualy large Coulomb matrix element (35 keV) between the analogue of the 64Zn ground state and the 64Ga ground state are discussed.