State highways, managed and built by state governments, function as significant intra-state routes.
Option A: Describes national highways, which support inter-state links.
Option B: Emphasizes that national highways or expressways handle such connections, not state highways.
Option C: Correct. State highways link a state's capital to its district headquarters and key towns.
Option D: Attributes this function to national highways.
Thus, the correct answer is (C): To link state capitals with district headquarters.