Harriette Walters, a former manager in the office, pleaded guilty last month to leading a scheme that drained more than $48 million from the city treasury over almost two decades.
Bank of America was the main bank used to deposit phony property tax refunds, and a former bank employee pleaded guilty in the scheme.
He was fired in February 2007 for violating bank standards of conduct, months before federal authorities made arrests in the case.
Bank of America should have alerted the city after it saw irregularities in the checks being deposited, D.C. officials alleged.
Bank of America had not had time to review the lawsuit, a spokeswoman for the bank said Friday.