We present a sample of 91 HI galaxies with little or no star formation and discuss the analysis of the integral field unit (IFU) spectra of 28 of these galaxies. We identified HI galaxies from the HI Parkes All-Sky Survey Catalog (HICAT) with Wide-field Infrared Survey Explorer (WISE) colours consistent with low specific star formation (< 10$^{-10.4}$ yr$^{-1}$), and obtained optical IFU spectra with the Wide-Field Spectrograph (WiFeS). Visual inspection of the PanSTARRS, Dark Energy Survey, and Carnegie-Irvine imaging of 62 galaxies reveals that at least 32 galaxies in the sample have low levels of star formation, primarily in arms/rings. New IFU spectra of 28 of these galaxies reveal 3 galaxies with central star formation, 1 galaxy with low-ionisation nuclear emission-line regions (LINERs), 20 with extended low-ionisation emission-line regions (LIERs) and 4 with high excitation Seyfert (Sy) emission. From the spectroscopic analysis of HI-selected galaxies with little star formation, we conclude that 75% of this population are LINERs/LIERs.