We report the synthesis of powder and single-crystal samples of cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of nonmagnetic Ce⁴⁺ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground-state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that Ce₂Hf₂O₇ is another candidate to investigate exotic correlated states of quantum matter, such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds Ce₂Sn₂O₇ and Ce₂Zr₂O₇.