We combine data from two all-sky surveys, the Swift/Burst Alert Telescope 22 Month Source Catalog and the AKARI Point Source Catalogue, in order to study the connection between the hard X-ray (> 10 keV) and infrared (IR) properties of local active galactic nuclei (AGN). We find two photometric diagnostics are useful for source classification: one is the X-ray luminosity vs. IR color diagram, in which type 1 radio-loud AGN are well isolated from other AGN. The second one uses the X-ray vs. IR color-color diagram as a redshift-independent indicator for identifying Compton-thick (CT) AGN. Importantly, CT AGN and starburst galaxies in composite systems can also be separated in this plane based upon their hard X-ray fluxes and dust temperatures. This diagram may be useful as a new indicator to classify objects in new surveys such as with WISE and NuSTAR.