The Evangelical-Lutheran Church of Norway, which has been Norway's official state church, has cut one -- but not all -- ties to the state. The national constitution now refers to it as the "national church" rather than the "state's public religion." Yet the key change is that the state will no longer appoint clergy for the church.
However, many other church-state ties remain in place, e.g., clergy are still considered civil servants, and the state will still fund the church. So this change is not an overly dramatic one. The state will still have a lot of influence in the church by being its primary source of funds. See this short article here.