Radio galaxies are uncommon γ-ray emitters, and only low-redshift radio galaxies are detected with the Fermi Large Area Telescope (Fermi-LAT). However, they offer potential insights into the emission mechanisms of active galaxies, particularly as the alignment of their jets with respect to the Earth means that, unlike blazars, their emission is not necessarily jet dominated. We use the Fermi-LAT data to perform an unbiased survey of 78 radio galaxies from the Bologna complete sample in order to search for new γ-ray-emitting radio galaxies. We observe statistically significant γ-ray emission from four of the six known Fermi-LAT-detected radio galaxies included in this sample, and find some evidence for γ-ray emission spatially coincident with four previously undetected radio galaxies. As a large parameter space is searched, we calculate a probability distribution to compute the look-elsewhere effect. We find that these four spatially coincident sub-threshold γ-ray excesses are most likely a chance association, and are unlikely to be emission from the radio galaxies. Upper limits on flux are calculated for the radio galaxies from which no γ-ray emission is observed.