An investment subsidiary of Citigroup will pay $4.5 million to 15,000 customers who were overcharged fees, including more than 600 on Long Island, under an agreement with New York State officials announced Wednesday morning.

The payment is the second to result from the state's investigation of Citigroup's Global Markets Inc. subsidiary. Including figures announced in October, Global Markets is now reimbursing more than $20 million in overcharged fees plus interest to more than 46,000 customers. The total includes $2 million to more than 5,600 New York State residents. A breakdown for Long Island of this larger group was unavailable.

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The office of state Attorney General Eric T. Schneiderman, which investigated the Citigroup unit, said the customers were overcharged when Global Markets failed to rebate certain accounts after periods of inactivity, when fees should not have been charged.

For certain types of investment accounts, Schneiderman's announcement said, Global Markets assessed fees at the beginning of a quarter for account management during the upcoming quarter. For a variety of reasons, a customer's account may be "frozen" during a particular period of inactivity. In some cases, customers should not be charged fees during that period, under the agreement between Schneiderman's office and Citigroup.

Citigroup's review revealed that if a customer requested a refund of fees paid covering a frozen period, Global Markets sometimes rebated the fees, but in thousands of cases it did not.

Citigroup said in a statement, "We are pleased to work with the New York Attorney General on this matter. We deeply regret the inconvenience to our clients, who will be reimbursed with interest."

The attorney general's investigation into Global Markets began in 2012 after a complaint from a Westchester resident and, Schneiderman said, has been done in cooperation with Global Markets.