Citigroup Inc.’s $301 billion of federal asset guarantees, extended by the U.S. last year to help save the bank from collapse, will be audited to calculate losses and determine whether taxpayers got a fair deal.

Neil Barofsky, inspector general of the U.S. Treasury Department’s $700 billion Troubled Asset Relief Program, agreed in an Aug. 3 letter to audit the program after a request by U.S. Representative Alan Grayson. Barofsky will examine why the guarantees were given, how they were structured and whether the bank’s risk controls are adequate to prevent government losses.

The Treasury, Federal Deposit Insurance Corp. and Federal Reserve provided the guarantees last November, when a plunge in Citigroup’s stock below $5 sparked concern that a run on the bank might rock global markets and impede an economic recovery. New York-based Citigroup paid the government $7.3 billion in preferred stock in return for the guarantees.

“What kind of toxic assets did the Federal Reserve guarantee, and what off-balance-sheet liabilities have been pinned on us?” Grayson, a Florida Democrat who sits on the House Financial Services Committee, wrote yesterday in an e- mailed response to questions on the audit. “How much money have the taxpayers already lost? We need to know.”

Citigroup’s guarantees are among $23.7 trillion of total potential government support stemming from programs set up since 2007 to ease the financial crisis, according to a report last month by Barofsky’s office.