State Government
Every Governor shall, before entering upon office, make and subscribe, in the presence of the Chief Justice of the relevant State High Court (or, in their absence, the senior-most available Judge), an oath or affirmation to faithfully execute the office, and to the best of their ability preserve, protect and defend the Constitution and the law, and devote themselves to the service and wellbeing of the people of that State.
A Governor's swearing-in oath is administered by the Chief Justice of that state's High Court - the state-level parallel to the President's oath being administered by the Chief Justice of India.
This is why a new Governor's swearing-in ceremony is typically conducted at the Raj Bhavan (Governor's residence) by the Chief Justice of that state's High Court, mirroring the President's own oath-taking process at the national level.