Previous studies found many climate properties such as northern hemisphere (NH) surface temperature and precipitation respond non-monotonically when CO2 is increased from 1x to 8xCO2 relative to pre-industrial levels. Here, we explore the robustness of the non-monotonicity in NH precipitation response in 11 coupled climate models. Eight models show a decrease of NH precipitation under repeated CO2 doubling beyond a critical level, which varies from 2xCO2 to 8xCO2. These models also show a robust cooling associated with the North Atlantic warming hole, and a prominent weakening in the Atlantic meridional overturning circulation (AMOC) at the same critical CO2 level. The sensitivity of NH precipitation and AMOC to CO2 doublings are positively correlated, especially when the AMOC weakens beyond 10 Sv. Regionally, this decrease in NH precipitation is most prominent over the North Atlantic, Europe and the tropical Pacific.