It is a common medical puzzler. The benefits statement arrives from the insurance company, saying that although the doctor has charged, say, $200 for that recent office visit, only $80 is covered , and the consumer is obliged to pick up the balance, the New York Times reports.

That gap may be too big, according to critics of the health insurance industry, whose ranks were joined Wednesday by the New York State attorney general, Andrew M. Cuomo.

Mr. Cuomo announced a sweeping investigation into whether health insurance companies have systematically forced patients to pay more than they should when using doctors and hospitals outside their insurer’s networks.

As part of the investigation, Mr. Cuomo said he intended to sue UnitedHealth Group, the state’s largest medical insurer and one of the nation’s biggest.

“We believe there was an industrywide scheme perpetuated by some of the nation’s largest health insurers to deceive and defraud consumers,” Mr. Cuomo said at a news conference on Wednesday.

Mr. Cuomo, who has conducted a number of recent inquiries aimed at health insurers, said that the practice had gone on for about a decade, potentially adding hundreds of millions of dollars to the out-of-pocket medical expenses of insured consumers nationwide.

UnitedHealth said it had done nothing wrong and was cooperating with the attorney general’s inquiry.

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