Are government agencies, such as a city, exempt from paying suta taxes?

The only thing I can offer is that I worked for a state government for many years and on several occasions, the state challenged former employees rights to collect unemployment benefits. Employers normally do that when it will cost them money if the former employee starts collecting benefits, and when the employer has grounds to show that the employee left his/her job voluntarily or is otherwise ineligible. That's not a very direct answer I realize, but based on what I saw I would say that governments do pay SUTA and it may vary by state.