Collinear laser spectroscopy on Cu58–75 isotopes was performed at the CERN-ISOLDE radioactive ion beam facility. In this paper we report on the isotope shifts obtained from these measurements. State-of-the-art atomic physics calculations have been undertaken in order to determine the changes in mean-square charge radii δ⟨r2⟩A,A′ from the observed isotope shifts. A local minimum is observed in these radii differences at N=40, providing evidence for a weak N=40 sub-shell effect. However, comparison of δ⟨r2⟩A,A′ with a droplet model prediction including static deformation deduced from the spectroscopic quadrupole moments, points to the persistence of correlations at N=40.