WASHINGTON  The inspector general who oversees the government’s bailout of the banking system is criticizing the Treasury Department for some misleading public statements last fall and raising the possibility that it had unfairly disbursed money to the biggest banks.

A Treasury official made incorrect statements about the health of the nation’s biggest banks even as the government was doling out billions of dollars in aid, according to a report on the Troubled Asset Relief Program to be released on Monday by the special inspector general, Neil M. Barofsky.

The report also provides new insight into the way the Treasury allocated billions of dollars to nine of Wall Street’s largest players. The report says that Bank of America appeared to qualify for more aid earlier, under the government plan. That assertion adds another element of intrigue to continuing investigations of the bank’s merger with Merrill Lynch and the role that regulators played in the deal, even as Merrill’s condition deteriorated.

The bailout formula called for banks to get an amount equal to as much as 3 percent of their risk-weighted assets, with aid capped at $25 billion for each institution, according to the report. By size, Citigroup, JPMorgan Chase and Bank of America could have qualified for more, and the first two received $25 billion.