We present the first fluorine measurements in 12 normal K giants belonging to the Galactic thin and thick disks using spectra obtained with the Phoenix infrared spectrometer on the 2.1 m telescope at Kitt Peak. Abundances are determined from the (1−0) R9 2.3358 μm feature of the molecule HF. Additionally, sodium abundances are derived in 25 giants in the thin disk, thick disk, and halo using the Na i line at 2.3379 μm. We report fluorine abundances for thin and thick disk stars in the metallicity range −0.7 < [Fe/H] < 0. We add two abundance measurements for stars with [Fe/H] < 0.5 dex, which are at a critical metallicity range to constrain models. We find a larger dispersion in fluorine abundances than sodium abundances despite both species having similar overall uncertainties due to atmospheric parameters, suggesting this dispersion is real and not observational. The dispersion is slightly larger in the thick disk than the thin. The thin and thick disk average [F/Fe] for our sample of stars combined with the literature differ by 0.03 dex. The observations are compared to available chemical evolution models.