Cross-identifying complex radio sources with optical or infrared (IR) counterparts in surveys such as the Australia Telescope Large Area Survey (ATLAS) has traditionally been performed manually. However, with new surveys from the Australian Square Kilometre Array Pathfinder detecting many tens of millions of radio sources, such an approach is no longer feasible. This paper presents new software (LRPY - Likelihood Ratio in PYthon) to automate the process of cross-identifying radio sources with catalogues at other wavelengths. lrpy implements the likelihood ratio (LR) technique with a modification to account for two galaxies contributing to a sole measured radio component. We demonstrate lrpy by applying it to ATLAS DR3 and a Spitzer-based multiwavelength fusion catalogue, identifying 3848 matched sources via our LR-based selection criteria. A subset of 1987 sources have flux density values for all IRAC bands which allow us to use criteria to distinguish between active galactic nuclei (AGNs) and star-forming galaxies (SFG). We find that 936 radio sources (~=47 per cent) meet both of the Lacy and Stern AGN selection criteria. Of the matched sources, 295 have spectroscopic redshifts and we examine the radio to IR flux ratio versus redshift, proposing an AGN selection criterion below the Elvis radio-loud AGN limit for this dataset. Taking the union of all three AGNs selection criteria we identify 956 as AGNs (~= 48 per cent). From this dataset, we find a decreasing fraction of AGNs with lower radio flux densities consistent with other results in the literature.