If that is true (do you have any references?). It probably vary between different regions. One explanation could be that due to the increase in CO2 emission there is an increase in biomass. This increase in biomass would absorb a lot of water from the ground and less water vapour is available to the atmosphere.
I agree with Mattias! In addition to this land management plays an important role in decreasing rain precipitation in certain areas of the world. I am thinking about the fast conversion of tropical forests to pasture to raise cattle, or large monocultures of banana, palm oil, sugarcane. Deforestation affects the water cycle because reduces water transpiration. Intensive tillage from agricultural land pumps more carbon into the atmosphere and amplifies this phenomenon.
The global temperature increase will lead to increased evaporation at the global scale, and thus to increased terrestrial annual average precipitations at the global scale. But at the local scale some regions will experience lower annual precipitation amounts.
This is the case with the regions located on the Western Pacific exposed to El Nino event concequences on the reduction of precipitation, if El Nino events increase, and if during non El NIno events the annual amount does not increase, and in a sens compensate the loss during El Nino events.