The Justice Department has agreed to investigate questions involving President Reagan's nominee to head the Government Printing Office before a Senate committee proceeds with his nomination.

The probe of Ralph E. Kennickell Jr. was first sought by Sen. Albert Gore Jr. (D-Tenn.). He has now been joined by Sens. Charles McC. Mathias Jr. (R-Md.) and Wendell H. Ford (D-Ky.).

The department has agreed to investigate what Gore calls "possible violations" of federal law surrounding "falsification of statements" on several government personnel forms. In addition, the senators have asked the department to probe how the folder containing Kennickell's personnel documents could not be located as Senate investigators asked to look at it.

The nomination has been put on hold until the investigation is completed. Kennickell still heads the GPO through a recess appointment he received last year.

"I'm staying, I've done nothing whatsoever wrong," Kennickell said in an interview Friday. He said he had "lifted the spirits of one of the most hard-boiled group of federal employes . . . in Washington."

Kennickell's road to the top of the GPO began in 1981, when, at the urging of Sen. Mack Mattingly (R-Ga.), he applied for the job of assistant public printer for planning. Then-Public Printer Danford Sawyer "turned a 20-minute welcome into a four-hour meeting," Kennickell recalled. But four days before Kennickell was to start work in September 1981, the White House Office of Presidential Personnel sent Sawyer a memo saying that Kennickell should not get the job.

Becky Norton Dunlop, then associate director of the office, wrote that the GOP leaders in Georgia were not able to substantiate the information that had been included with Mr. Kennickell's paperwork." The memo also noted that Kennickell had voted in the 1980 Democratic primary.

Kennickell told the White House that he had filed with the Democrats because the GOP ticket in Savannah was unopposed, and he wanted to vote against an incumbent district attorney, who was a Democrat. Later, White House political aide Lee Atwater confirmed Kennickell's Republican credentials and tried to place him at other agencies, but with no success. Atwater then suggested that Kennickell be given a job as a consultant to the Treasury Department.

When he filled out the government personnel form, when he first talked with Sawyer, Kennickell stated that he was paid $20,929 in his last year at the family-owned Kennickell Printing Co.

But when he filled out the form at Treasury in December 1981, Kennickell added a $30,000 bonus that he said his father told him the previous month that he would receive. That brought his salary to about $50,000, the rate the Treasury Department then decided to pay him.

Kennickell never received the bonus, but continued to include it when he filled out the form three more times for jobs at the Small Business Administration and his current position.

But investigators said that Kennickell's father, Ralph Kennickell Sr., told them he never planned to give his son a bonus. The GPO nominee said his father was "misled" and "badgered" by committee investigator Gerald R. Gereau.

Gereau said he asked the question "three ways" to make sure the elder Kennickell understood. "He answered clearly," Gereau said. "There was to be no bonus."

A June 26 letter from the senior Kennickell to Mathias said Gereau asked only about a written agreement for a bonus. "I said no," the elder Kennickell said. "I told your investigator Ralph and I did not need to write letters about these things like you people in Washington are always doing to each other."

In trying to sort through the issues, Gereau sought Kennickell's personnel file to clarify the confusing salary figures. The file, however, is missing from GPO.

Kennickell said it "was taken by someone trying to embarrass me."