Carol S. Greenwald resigned yesterday as president of the National Consumer Cooperative Bank. No immediate successor was named.

Her resignation, which was expected, will become effective Jan. 31 when her three-year contract expires. She has accepted a position as a guest scholar at the Brookings Institution.

Greenwald, an outspoken and controversial administrator, has been on sabbatical since Nov. 1. Since then, the bank's executive vice president, Mitchell Rofsky, has been acting president and chief executive officer. He will continue in this post until a new chief is chosen. The board said yesterday it hopes to complete its search by June.

Greenwald plans to retain some ties to the bank by serving as chairman of its financial advisory committee. Chairman Frank Sollars declared, "We appreciate the many contributions she made during the three years she served as president, and we are pleased she will continue to assist the bank in its financial planning."

Greenwald, an economist who had previously made a reputation in Massachusetts and Washington as a consumer-oriented banking commissioner, was the first president of the Co-op Bank, chartered by Congress in 1978 to provide credit and financial support to consumer and other types of cooperatives. Her tenure was marked by policy differences between the board of directors, which wanted to act like a conventional bank, and consumer organizations, which criticized it for not being more generous.

When the Reagan administration tried to abolish the bank, Greenwald defied OMB Director David Stockman by withdrawing $60 million from the Treasury and putting it in the bank's checking account.

Internal clashes also occurred. There was an unsuccessful attempt by employes to form a union. Moreover, there was a considerble turnover of employes under Greenwald.

Rumors of her departure spread last fall after the October board meeting. A director who asked not to be identified said at the time that Greenwald would be "phased out." Soon after that, it was announced that she would take a leave and thereafter would be offered an additional 18 months' work at the bank in an unspecified capacity.

The director said the bank was operating in the black but had been obliged to write off a number of bad loans to cooperatives. Congress established the Co-op Bank with an initial government investment of $200 million. The General Accounting Office is conducting a general audit of the bank.

Earlier this month, House Banking Committee chairman Rep. Fernand J. St Germain (D-R.I.) revealed information from a secret bank examination showing that nearly one-quarter of the loans in the Co-op Bank's $72 million portfolio were classified as problems.

The report further stated, "Although the poor quality of the bank's loan portfolio may have resulted partly from a business and lending philosophy deliberately formed with a greater tolerance for risk than was acceptable to conventional lenders, the causes more easily discerned by the examiners were deficiencies in organization and in the capabilities and performance of credit staff."

St Germain plans to hold oversight hearings on the bank early in the next congressional session.