The Constitution of the United States of America does not mention local governments.  Local governments are created by and regulated by the states.  This means that to speak about cities or other forms of local government in the United States is to speak about fifty different legal and political situations.

The states outline the powers of municipal governments in charters.  There may be:

• special or specific charters;
• general or classified charters (in which the rules may apply to a class of cities,
  often grouped by population size); or
• home rule charters.

The state municipal leagues can provide information about the form of charter provided by the state constitutions.

One court decision, referred to as "Dillon's Rule" has been applied to municipal powers in many states.   Dillon's Rule is derived from written decision by Judge John F. Dillon of Iowa in 1868.  It is a cornerstone of American municipal law.  It maintains that a political subdivision of a state is connected to the state as a child is connected to a parent.  Dillon's Rule is used in interpreting state law when there is a question of whether or not a local government has a certain power.  Dillon's Rule narrowly defines the power of local governments.

The first part of Dillon's Rule states that local governments have only three types of powers:

• those granted in express words,
• those necessarily or fairly implied in or incident to the powers expressly granted, and
• those essential to the declared objects and purposes of the corporation, not simply convenient, but indispensable.

The second part of Dillon's Rule states that if there is any reasonable doubt whether a power has been conferred on a local government, then the power has NOT been conferred.  This is the rule of strict construction of local government powers.

Source:
Clay Wirt. "Dillon's Rule."  Virginia Town & City. August 1989, vol. 24 no. 8, pp 12-15.