Sen. David F. Durenberger has his father-in-law, Edward Baran, working in the senator's Washington office at $1,600 a month. Durenberger is tapping his $175,000 campaign fund surplus to pay Baran, a former District of Columbia tax administrator.

Federal law prohibits officials from hiring relatives who might be paid with federal money, but Thomas F. Horner, the senator's press secretary, said today that Baran was hired as a temporary consultant from May 18 to Nov. 1.

"This is allowed for in the Senate rules," Horner said. "I know very well other senators have hired consultants on various projects." Horner said the only prohibition was against the hiring of relatives with official Senate funds.

Baran, 62, was hired without a written contract, Horner said in a telephone interview.

Baran was hired to improve mail-handling procedures in constituent correspondence. His job was reported today in The Minneapolis Tribune.

Senate rules permit members to hire experts and interns from private organizations, universities or corporations on a temporary basis as long as they paid with private funds. The Senate Select Committee on Ethics has ruled that such aides are not entitled to fringe benefits customarily available to official employes of the Senate.

Baran was associate director for assessment administration in the District of Columbia from 1967 to 1975. Thereafter, he was city assessor in Petersburg, Va., from 1978 until early 1980.