We investigate the tunability of optofluidic distributed feedback (DFB) dye lasers. The lasers rely on light-confinement in a nano-structured polymer film where an array of nanofluidic channels constitutes a third order Bragg grating DFB laser resonator with a central phase-shift. The lasers are operated by filling the DFB laser resonator with a dye solution by capillary action and optical pumping with a frequency doubled Nd: YAG laser. The low reflection order of the DFB laser resonator yields low out-of-plane scattering losses as well as a large free spectral range (FSR), and low threshold fluences down to similar to 7 mu J/mm2 are observed. The large FSR facilitates wavelength tuning over the full gain spectrum of the chosen laser dye and we demonstrate 45 nm tunability using a single laser dye by changing the grating period and dye solution refractive index. The lasers are straight-forward to integrate on lab-on-a-chip microsystems, e. g. for novel sensor concepts, where coherent light in the visible range is desired.