NEW YORK – Of all the bank fees that customers love to hate, overdraft charges on checking accounts have to be near the top. The government’s new consumer protection agency appears to agree.

The Consumer Financial Protection Bureau said Wednesday that it will investigate overdraft fees, including how they are marketed and explained to customers. The agency said the probe could result in additional rules, perhaps even lawsuits.

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Richard Cordray, director of the Consumer Financial Protection Bureau, testifies last month before the Senate Banking Committee. The Associated Press

Overdraft fees are charged by banks when customers try to spend more money than they have in an account. Banks will allow the transaction, then charge the customer a penalty of as much as $35.

“We’ve heard many stories about the $40 cup of coffee,” the agency’s director, Richard Cordray, told reporters and representatives from banks and consumer groups.

Cordray and representatives from four consumer advocacy groups said that the overdraft fees hurt the people who can least afford them because poorer customers are more likely to drain their checking accounts to close to zero.

Since the 2008 financial crisis, the government has clamped down on bank practices that it considers unfair, such as marketing credit cards to teenagers. Banks have complained some of the government’s moves have been too intrusive.

In 2010, the Federal Reserve barred banks from automatically enrolling customers in so-called overdraft protection programs for debit card or ATM transactions. Without overdraft protection, a transaction is declined if the customer can’t cover it.

The rule did not apply to checks, online bill payments or recurring debits, such as having the monthly cable bill automatically sent to your debit card. It also did not limit how much banks can charge for the service.

Banks have responded by marketing overdraft protection aggressively. Some told customers that opting out of overdraft protection could prevent them from making everyday transactions, including “medical or health emergencies,” according to research published last year by the Center for Responsible Lending, a consumer group that opposes overdraft fees.

Banks collected $29.5 billion in revenue from overdraft fees in 2011, according to research firm Moebs Services. That was down from $33.1 billion in 2010 but a significant increase from $18 billion in 1999, when the fees were less common.

Cordray said the problem is not just the fees but that banks often don’t explain them clearly. One bank, which he did not name, required customers to visit three different websites and scroll through 50 pages of dense text just to get an explanation, he said.

Cordray praised banks for finding ways to help customers avoid the fees, such as not charging overdrafts for purchases of less than $5 or giving customers 24 hours to add more money to an account.

Representatives of consumer groups who appeared with Cordray said customers would rather have their cards declined than be charged the fee. A representative of Citigroup, one of the country’s largest banks, said customers prefer to avoid the embarrassment.

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