Final answer:
The primary level of party organization involved in registering voters is the County or Regional Party Committee, which handles critical ground-level work in the democratic process.
Step-by-step explanation:
The level of party organization that is primarily involved in registering voters is C) County or Regional Party Committee. Within the party structure, this level frequently engages in essential democratic processes, such as identifying and mobilizing potential voters and donors, which include the task of voter registration. While the national and state party committees have more visibility, especially during presidential elections, the county or regional party committees are often the workhorses of the party system, carrying out the critical ground-level work that underpins electoral success.