Ultraluminous X-ray sources (ULXs) were once largely believed to be powered by super-Eddington accretion onto stellar-mass black holes, although in some rare cases, ULXs also serve as potential candidates for (sub-Eddington) intermediate-mass black holes. However, a total of eight ULXs have now been confirmed to be powered by neutron stars, thanks to observed pulsations, and may act as contaminants for the radio/X-ray selection of intermediate-mass black holes. Here, we present the first comprehensive radio study of seven known neutron star ULXs using new and archival data from the Karl G. Jansky Very Large Array and the Australia Telescope Compact Array, combined with the literature. Across this sample, there is only one confident radio detection, from the Galactic neutron star ULX Swift J0243.6+6124. The other six objects in our sample are extragalactic, and only one has coincident radio emission, which we conclude is most likely contamination from a background H ii region. We conclude that with current facilities, neutron star ULXs do not produce significant enough radio emission to cause them to be misidentified as radio-/X-ray-selected intermediate-mass black hole candidates. Thus, if background star formation has been properly considered, the current study indicates that a ULX with a compact radio counterpart is not likely to be a neutron star.