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 in state constitutions.

Revising Charters - An Example from New York State

The following example of the charter revision process for New York State illustrates how one state allows charters to be changed.  There are three ways to revise a city charter in the state of New York:

1) Charter Commission
A charter commission may be established by any of three procedures: 

A) The city's legislative body may establish a charter commission, or it may submit to the city voters the question of whether or not there shall be a charter commission.  The council must indicate the number of members on the commission and whether the members shall be elected or appointed.

B) The mayor of a city may create a charter commission by appointing no less than nine members. The commission is established upon the filing with the city clerk of the mayor's certificate of appointment, which also will name the chairman, vice chairman and secretary. 

C) The establishment of a commission by voter initiative requires signatures equal to 15 percent of the votes cast within the city for Governor at the last gubernatorial election -- or 45,000, whichever is less.  The legislative body is then required to submit the matter to a referendum. 

After a charter commission has been created, it must review the entire charter and prepare a draft of proposed revisions. The proposed amendments are to be completed and filed with the city clerk in time for submission to the voters at the next general or a special election.

2) Initiative and Referendum
If a number of city voters equals to at least 10 percent of the votes cast for Governor in the last gubernatorial election -- or 30,000, whichever is less -- sign a petition for a new charter or charter amendments, the initiative process is under way. The petition and proposed charter changes are filed with the city clerk, and submitted for judicial review.  If the proposed changes require a referendum, the legislative body may submit the proposal to the voters at the next general election.

3) Direct Legislative action 
A city charter can be revised by direct action of the legislative body under its local law power.

Source:
James A. Coon.  Revising City Charters in NY State. Local Government Technical Series. Albany, NY: New York State Department of State, Division of Local Government Services, June 1998.