Nope.
Federal and State governments may, local governments do not.
Where did you get such a silly notion?
"[T]he doctrine of sovereign immunity is "alive and well" in Virginia." "Though this Court has, over the years, discussed the doctrine in a variety of contexts and refined it for application to constantly shifting facts and circumstances, we have never seen fit to abolish it. Nor does the General Assembly want the doctrine abolished." ... "One of the most often repeated explanations for the rule of state immunity from suits in tort is the necessity to protect the public purse. However, protection of the public purse is but one of several purposes for the rule." Messina v. Burden, 228 Va. 301 (1984)
"It is well established that the doctrine of sovereign immunity protects municipalities from tort liability arising from the exercise of governmental functions." Niese v. City of Alexandria, 264 Va. 230 (2002).