Final answer:
The secretary of state is responsible for maintaining public records and overseeing elections within a state's executive branch.
Step-by-step explanation:
The executive branch official who maintains public records and administers elections is the secretary of state. This role involves overseeing the proper recording of official documents, such as laws and the governor's official acts, and managing the electoral process. The legislature designates the secretary of state with the responsibility for supervising elections as well as handling corporate and similar filings. In contrast, the attorney general is the state's chief legal officer, the lieutenant governor often acts as the president of the state senate and assumes gubernatorial duties if needed, and the state auditor is responsible for overseeing the financial integrity and compliance of government operations.