Phonosemantic compound. 宀 represents the meaning and 元 represents the sound. The 宀 component is used because putting on a roof completes the process of constructing a building.

The characters 史 (history), 吏 (government official), 使 (cause; use; instruct), and 事 (matter; work; affair) are all etymologically related and all derive from the same ancient character, depicting a hand (又) holding a container for writing utensils. 事 and 史 were originally written the same, but later an extra mark was added to distinguish them.