If the territory included inside the boundaries of the annexing district consists of all of a single county and the territory to be annexed consists of all of an adjacent county, the adjacent territory may be annexed in the manner provided in Sections 62.291-62.306 of this code, except the commissioners court of the county to be annexed shall:
(1) conduct the hearing;
(2) order the election;
(3) canvass the returns of the election; and
(4) perform all other duties provided by this subchapter for the commission of the annexing district.