President Carter is expected to sign an executive order today naming his wife, Rosalynn, to head a commission to examine the state of the nation's mental health and its care for the mentally ill.

The appointment had been expected as Mrs. Carter said during the presidential campaign that, if her husband were elected, she would make mental health a major interest as part of being an active First Lady.

What she will undertake may be a greater official role in advising the government than any previous First Lady.

She will chair a 20-member commission that will be asked by the President to examine the way the country is spending $37 billion a year on mental and emotional care.

The commission will be directed to make a preliminary report by Sept. 1 and a final one by April 1, 1978, according to administration sources.

No such major look at mental care in America has been taken since 1955, and the commission will face many tough questions occupying mental health workers.

A leading one, said a White House aide, is whether the drive to empty the nation's mental hospitals has gone too far - and whether communities are taking proper care of the thousands of disturbed people discharged from state hospitals to their hometowns care.

Twenty years ago 77 per cent of the mentally ill were cared for in hospitals. Today the figure is 30 per cent.

Many discharged patients are crowded into substandard nursing homes and "welfare hotels." Congress has decreed that the government should create 1,500 community mental-health centers to give continued care, but only about 600 have been started.

Another problem the commission is expected to examine is the extent to which the government should spend money to train psychiatrists who then care for private patients at high fees rather than giving public service. Still another is how far any future national health insurance should go to cover mental care.

Both problems are subjects of debate. Some health-insurance proposals include no more than 30 days' mental care, though it is one of the most common illnesses.