We investigate the 1.4 GHz radio properties of 92 nearby (z<0.05) ultra hard X-ray selected Active Galactic Nuclei (AGN) from the Swift Burst Alert Telescope (BAT) sample. Through the ultra hard X-ray selection we minimise the biases against obscured or Compton-thick AGN as well as confusion with emission derived from star formation that typically affect AGN samples selected from the UV, optical and infrared wavelengths. We find that all the objects in our sample of nearby, ultra-hard X-ray selected AGN are radio quiet; 83% of the objects are classed as high-excitation galaxies (HEGs) and 17% as low-excitation galaxies (LEGs). While these low-z BAT sources follow the radio--far-infrared correlation in a similar fashion to star forming galaxies, our analysis finds that there is still significant AGN contribution in the observed radio emission from these radio quiet AGN. In fact, the majority of our BAT sample occupy the same X-ray--radio fundamental plane as have been observed in other samples, which include radio loud AGN --- evidence that the observed radio emission (albeit weak) is connected to the AGN accretion mechanism, rather than star formation.