The powerful jets of blazars have been historically considered as likely sites of high-energy cosmic-ray acceleration. However, the particulars of the launched jet and the locations of leptonic and hadronic jet loading remain unclear. In the case when leptonic and hadronic particle injection occur jointly, a temporal correlation between synchrotron radiation and neutrino production is expected. We use a first catalog of millimeter wavelength (95–225 GHz) blazar light curves from the Atacama Cosmology Telescope for a time-dependent correlation with 12 yr of muon neutrino events from the IceCube South Pole Neutrino Observatory. Such millimeter emission traces activity of the bright jet base, which is often self-absorbed at lower frequencies and potentially gamma-ray opaque. We perform an analysis of the population, as well as analyses of individual, selected sources. We do not observe a significant signal from the stacked population. TXS 0506+056 is found as the most significant, individual source, though this detection is not globally significant in our analysis of selected active galactic nuclei. Our results suggest that the majority of millimeter-bright blazars are neutrino dim. In general, it is possible that many blazars have lighter, leptonic jets, or that only selected blazars provide exceptional conditions for neutrino production.