how did the sumarians link religion and government

Through the ruler/king/city-state leader. The Sumerian ruler had to show how he was divinely chosen for his ruling, so he oftentimes named himself the father of the country and had himself portrayed as the middle guy or messenger between the gods - they were polytheistic with Zeus, Hera, Poseidon, and others -  and the people.  

They believed in having rulers rule each city-state separately, unless when in war and or have mutual needs.
Hope this helps!