In this study, we present high-resolution VIsible Multi-Object Spectrograph integral field unit spectroscopy (VIMOS-IFU) of the extremely metal-poor H ii/blue compact dwarf (BCD) galaxy Tol 65. The optical appearance of this galaxy shows clearly a cometary morphology with a bright main body and an extended and diffuse stellar tail. We focus on the detection of metallicity gradients or inhomogeneities as expected if the ongoing star formation activity is sustained by the infall/accretion of metal-poor gas. No evidences of significant spatial variations of abundances were found within our uncertainties. However, our findings show a slight anticorrelation between gas metallicity and star formation rate at spaxel scales, in the sense that high star formation is found in regions of low metallicity, but the scatter in this relation indicates that the metals are almost fully diluted. Our observations show the presence of extended Hα emission in the stellar tail of the galaxy. We estimated that the mass of the ionized gas in the tail M(H ii)tail ∼1.7 × 105 M⊙ corresponds with ∼24 per cent of the total mass of the ionized gas in the galaxy. We found that the Hα velocity dispersion of the main body and the tail of the galaxy are comparable with the one found in the neutral gas by previous studies. This suggests that the ionized gas still retains the kinematic memory of its parental cloud and likely a common origin. Finally, we suggest that the infall/accretion of cold gas from the outskirts of the galaxy and/or minor merger/interaction may have produced the almost flat abundance gradient and the cometary morphology in Tol 65.