We investigate thin insulating CaF2 films on a Si (111) surface using a combination of noncontact atomic force microscopy (NC-AFM) and Kelvin probe force microscopy (KPFM). Atomic-scale NC-AFM and KPFM images are obtained in different imaging modes by employing two different tip polarities. The KPFM image contrast and the distance-dependent variation of the local contact potential difference (LCPD) give rise to a tip-polarity-dependent contrast inversion. Ca2+ cations had a higher LCPD contrast than F- anions for a positively terminated tip, while the LCPD provided by a negatively charged tip gave a higher contrast for F- anions. Thus, this result implies that it is essential to determine the tip apex polarity to correctly interpret LCPD signals acquired by KPFM.