State highways are major intra-state roads built and managed by state governments.
Option A: This description aligns with national highways, which support inter-state travel.
Option B: The role described is typically fulfilled by national highways or expressways, not exclusively by state highways.
Option C: Correct. State highways link a state's capital to its district headquarters and significant towns.
Option D: This function is primarily associated with national highways.
So, the correct answer is (C): To connect state capitals with district headquarters.