The Pleasanton school board took no action after meeting for more than an hour in closed session Tuesday night to discuss unspecified employee discipline and anticipated litigation.
It was the board's second special closed-session meeting in just over a week.
On Dec. 19, the board placed Superintendent Rick Rubino on paid administrative leave following a closed-session meeting with an agenda stating the board would hold discussions on "public employee discipline/dismissal/release" and two potential court cases.
The closed-session agenda for Tuesday night's meeting mirrored that of the Dec. 19 meeting, but it's not known whether trustees talked about the superintendent again.
District officials have said Rubino was placed on leave pending the outcome of an investigation into a personnel matter but have declined to elaborate further.
It's not known how long the investigation will take, but the district is in the process of hiring an independent investigator to handle it. That investigator will report to the school board, district officials said.
The board's next regularly scheduled meeting is Jan. 17.