Variations in the CO2 dissolved in water springs have long been observed near the epicenters of moderate and strong earthquakes. In a recent work focused on data collected during the 2017–2021 period from a monitoring site in the Northern Apennines, Italy, we noticed a significant correlation between CO2 anomalies and moderate-to-weak seismic activity. Here, we extended this analysis by focusing on data collected from the same site during a different period (2010–2013) and by integrating the CENSUS method with an artificial neural network (ANN) in the already-tested protocol. As in our previous work, a fit of the computed residual CO2 distributions allowed us to evidence statistically relevant CO2 anomalies. Thus, we extended a test of the linear dependence of these anomalies to seismic events over a longer period by means of binary correlations. This new analysis also included strong seismic events. Depending on the method applied, we observed different time lags. Specifically, using the CENSUS methodology, we detected a CO2 anomaly one day ahead of the earthquake and another anomaly eleven days ahead. However, no anomaly was observed with the ANN methodology. We also investigated possible correlations between CO2 concentrations and rain events and between rain events and earthquakes, highlighting the occurrence of a CO2 anomaly one day after a rain event of at least 10 mm and no linear dependence of seismic and rain events. Similar to our previous work, we achieved a probability gain of around 4, which is the probably of earthquake increases after CO2 anomaly observations.