For the purposes of this chapter, the "appropriate party committee" shall be defined as:
I. The state committee of that party or, if previously authorized by the same, the executive committee thereof for the offices of United States senator, United States representative, governor, councilor and state senator.
II. The county committee of that party for county offices and state representative if from a representative district containing more than one town, ward, or unincorporated place.
III. The town or ward committee of that party for state representative if the representative district contains only the town or ward.