The Securities and Exchange Commission, which must decide by November whether to permit the big brokerage firm E. F. Hutton & Co. to keep its status as an investment adviser, yesterday was given permission to examine grand jury testimony that led to Hutton's guilty plea last month to a multibillion-dollar check-kiting scheme.

If the SEC should vote to remove Hutton's authority to act as an investment adviser, the giant brokerage firm, with hundreds of thousands of customers and billions of dollars of funds under management, might have to close its doors.

Under a 1940 law, a convicted felon is barred automatically from being an investment adviser unless the SEC determines there is a reason to waive the requirement. The SEC gave Hutton a six-month waiver last month because Hutton had so many customers and so much money under management that to do otherwise would have harmed hundreds of thousands of innocent investors.

The SEC now will investigate whether to grant Hutton a permanent waiver. SEC Chairman John S. R. Shad, who was a top official at Hutton during part of the period the check-kiting scheme operated, has recused himself from the investigation. Shad, who was interviewed by the Justice Department during its three-year investigation of Hutton, has said he knew nothing of the check fraud.

U.S. District Judge William Nealon in Scranton, Pa., yesterday signed an order that gives top SEC officials access to grand jury documents and testimony, but also requires that witnesses be notified and given the right to object to the disclosure of testimony.

The grand jury heard testimony from about 300 persons, many of them Hutton and bank employes, and subpoenaed millions of pages of documents.

Hutton, one of the biggest U.S. securities firms, pleaded guilty to 200 counts of mail fraud and wire fraud last month, paid a $2 million fine, $750,000 in Justice Department expenses and agreed to make restitution to banks it defrauded.

Justice officials said Hutton tricked banks into making billions of dollars of loans during a 20-month period from July 1980 until February 1982. In the process, officials said, Hutton cheated the banks out of tens of millions of dollars in interest.

No individuals were required to plead guilty in the check-kiting scheme, a fact that a number of senators and others have criticized

Assistant U.S. Attorney Albert Murray, who was the lead prosecutor, said a number of other companies engage in similar practices and that they present a risk to the health of the banking system.