We present the first data release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA)-Arizona Radio Observatory (ARO) Survey of CO Targets (MASCOT), a European Southern Observatory public spectroscopic survey conducted at the ARO. We measure the CO(1-0) line emission in a sample of 187 nearby galaxies selected from the MaNGA survey that has obtained integral field unit (IFU) spectroscopy for a sample of similar to 10000 galaxies at low redshift. The main goal of MASCOT is to probe the molecular gas content of star-forming galaxies with stellar masses >10(9.5)M(circle dot) and with associated MaNGA IFU observations and well-constrained quantities like stellar masses, star formation rates, and metallicities. In this paper, we present the first results of the MASCOT survey, providing integrated CO(1-0) measurements that cover several effective radii of the galaxy and present CO luminosities, CO kinematics, and estimated H-2 gas masses. We observe that the decline of the galaxy star formation rate with respect to the star formation main sequence increases with the decrease of molecular gas and with a reduced star formation efficiency, in agreement with results of other integrated studies. Relating the molecular gas mass fractions with the slope of the stellar age gradients inferred from the MaNGA observations, we find that galaxies with lower molecular gas mass fractions tend to show older stellar populations close to the galactic centre, while the opposite is true for galaxies with higher molecular gas mass fractions, providing tentative evidence for inside-out quenching.