Yes, the Board of Governors, the 12 Federal Reserve Banks, and the Federal Reserve System as a whole are all subject to several levels of audit and review:
In addition, the Reserve Banks are subject to annual examination by the Board. The Board's financial statements and the combined financial statements for the Reserve Banks are published in the Board's Annual Report.
See our audit page for more information on all of the above audits and more information on the accounting, financial reporting, and internal controls of the Federal Reserve Board and Federal Reserve Banks.