Churches in the United States have a tendency toward congregationalism as their form of government. That is, property is owned by the local congregation, and all decisions reside with that body. It's a form of democratic governance that has not always been the case. Roman Catholic, Episcopal, and United Methodist churches are different, in that the local property belongs to the larger denomination. In United Methodist Churches in particular it's said that local property is held "in trust" for the denomination. The congregation can leave the denomination if they want, for example, but the property stays with the denomination. The American National Catholic Church (ANCC), by contrast, practices congregational autonomy.
Most evangelical and Pentecostal churches in our times seem to be congregational. This is especially the case with "non-denominational" churches. It grants a certain freedom to the local church, although it can also remove accountability. People in a local church have no higher recourse than their own board to intervene when something goes wrong, like when a pastor is abusive.
While the ANCC practices congregational polity, the clergy are still hierarchical. All the priests share in the ministry of the head bishop, wherever they may be serving locally. So while a congregation can join or leave the ANCC at any time, they won't necessarily have their same priest if they do so. Priests joining the ANCC have to be incardinated, while a congregation leaving the ANCC might not be able to persuade its priest to go along. And besides, who would be the priest's bishop in this situation?
