Robert T. Griffin, fired as deputy administrator of the General Services administration in July, has threatened to sue GSA if it turns over his notes, diaries, telephone logs and other materials to internal investigators.

In a letter to GSA Administrator Jay Solomon on Tuesday, Griffin demanded that GSA turn over the records from his GSA office to his lawyer and refrain from examining the records unless they are subopenaed. Griffin contended that such records have been recognized GSA in the past as being personal rather than government property.

Griffin now works in the White House, where he was given a $50,000 job after his friend and political patron, House Speaker Thomas P. (Tip) O'Neill Jr., complained to President Carter that Griffin had been treated "shabbily" in his dismissal by Solomon from the number two GSA job.

It also has been learned that the records of another GSA official, Jerald Sternburg, who was in charge of the GSA stores that provided government workers in the Washington region with office supplies, have been subpoenaed by a federal grand jury in Baltimore.

The grand jury which has been investigating bribery of GSA supply store managers by office supply firms doing business with GSA, has already indicted 18 store managers and other persons, eight of whom have pleaded guilty to defrauding the government. Those eight are now cooperating with federal prosecutors in Baltimore who are trying to trace the corruption to "higher-ups" to GSA.

Sternburg, who was Washington regional commissioner of GSA's federal supply service, had been given another job in GSA recently. He had no comment on the subpoenaing of his records.

The controversy surrounding Griffin's records arose when Vincent R. Alto, a former Justice Department prosecutor hired by Solomon to oversee internal investigations of corruption in GSA, wanted to examine Griffin's desk calendar and logs made by his secretaries of incoming and outgoing calls.

Alto, according to well-informed sources, wanted to determine whether Griffin had any part in a GSA decision to award a contract to Art Metal-USA Inc. to supply GSA with chairs even though GSA knew the chairs did not meet its specifications. On the day the $5.5 million contract was approved. Solomon was out of town and Griffin was acting administrator.

Griffin, who declined to comment on his letter to Solomon about the records, said last night, "I have had no connection with Art Metal since I entered GSA."

Art Metal, a Newark, N.J., firm that specializes in selling metal desks and file cabinets to GSA, has been the subject of GSA investigations because of the insistence of some GSA officials on buying from the firm despite repeated complaints about the quality of its office furniture.

When GSA investigators attempted to examine Griffin's records two weeks ago, the GSA official in charge of them objected that they were personal, the sources said. Alto, citing a court decision, overruling Henry Kissinger's attempt to retain transcripts of telephone calls made by his secretaries when he was secretary of state, said Griffin's records were government property. However, a GSA lawyer contended they were personal, and Griffin subsequently learned about the dispute within GSA.

"I hereby demand that all of my private property above-described be delivered forthwith to my attorney, William P. Daisely at the firm of King & Nordinger . . . and that you refrain from examining my private papers without receipt of the above-mentioned process," Griffin wrote Solomon.

"You are further notified that if GSA (a.) refuses to deliver the documents in question as requested within three days of this letter, or (b.) you cause or allow my propoerty to be examined without due process under the Constitution of the U.S. and applicable statutes, I will feel free to file appropriate legal action as I may be advised."

Daaisley last night said Griffin does not want "official records" but only those he considers personal, such as personal checkbooks. "He does not know the nature of the material GSA is withholding, and it is impossible to comment specifically on what records are involved;" Daisley said.

Some of Griffin's records are no longer at GSA. One of Griffin's aides, Peter M. Mollica, took two boxes of Griffin's personal materials, including personal checkbooks and pictures, out of GSA after Griffin was dismissed.

Griffin is now a senior assistant to Robert S. Strauss, President Carter's special trade representative and counselor on inflation. Griffin, who receives the same salary as at GSA, is expected next year to make use of his contacts in Congress to help obtain passage of trade legislation.