This is what I always use. It looks like a code smell, but it's extremely easy to read and even someone that just learned Python yesterday can understand what's happening.

If I need a lot of state, I'll make a class to go with it. But usually it's just your example.

One variation I use is if you don't want the connection module knowing how to get the connection settings, you can make another method like init_connection(settings) and then get_connection() just throws a RuntimeError if it's not initialized yet.

  _connection = None

  def init_connection(settings):
    global _connection
    _connection = create_connection(settings)

  def get_connection():
    if not _connection:
      raise RuntimeError("Connection must be initialized before trying to use it. Make sure you call init_connection() in your startup.")
    return _connection