US national and state capitol (with an o) buildings are located in the federal and state capital (with an a) cities.

Thirty-nine states name the state administrative and legislative building – the place where the governor has their office – “State Capitol”. Indiana and Ohio call it a “Statehouse” (both words joined) while Maine, Maryland, Massachusetts, New Hampshire, New Jersey, Rhode Island, South Carolina, and Vermont use “State House” (two separate words) . Delaware has a “Legislative Hall”. The State of Alabama has a State Capitol, but the Legislature meets in the State House.

Most State Capitols are working buildings, but in Arizona the Arizona State Capitol is used as a museum, and both the legislature and the governor’s office are in nearby buildings

In Indiana, Kentucky, Nebraska, North Dakota, Oklahoma, Pennsylvania, South Dakota, West Virginia, and Wisconsin the supreme courts are in the capitols.

For most states, the classical dome is the central feature of the capitol, but not in Alaska, Florida, Hawaii, Louisiana, New Mexico, New York, North Dakota, Ohio, Oregon, Tennessee and Virginia state capitols.