Latin caput (head): capitalis, of the head, hence chief city (caput mundi, Rome was head of the world), hence capital offense (losing the head), and through medieval capitale (property, stock), wealth counted in heads of cattle. Chapter, captain, chief, and cap all ride the same root.
The livestock logic: wealth was counted in head of cattle, so capital is literally your herd counted by skulls. English cattle and chattel are the same word, capitale, imported twice through Norman French at different centuries.
Caput descends from PIE *kaput (head), cousin to English head itself and to German Haupt. That the words for money, governance, and execution share a skull is either a coincidence of anatomy or a standing summary of what the state does.
Why does the same word govern your money, your city, and your neck?