Last December Jeff Butler of McLean, a novice car mechanic, plunked down $125 for an inoperable 1963 Citroen. Butler towed the car home and eventually got it to run continuously for about six weeks earlier this year, when it surprised no one by breaking down again.

Since then, with Citroen parts hard to find, the low-slung, white vehicle has been sitting in the Butler driveway, its motor gone, the back glass broken and several dents in the doors.

"It's the ugliest looking thing. It wouldn't give anybody 2 cents for it," Jeff's mother, Alice Butler commented yesterday.

The Fairfax County office of Assessments has taken a different view. This months, implementing a major reason the assessors felt were undervalued, assessment of older cars, some of which the value of Butler's Citroen was set at $2,050, which makes the annual personal property tax due on it $103.20.

"It's really ridiculous. It just doesn't make any sense to me," said Mrs. Butler, one of a number of persons who have taken similar complaints to the Fairfax County Board of Supervisors.

Yesterday, the board ordered the assessment staff to look into the matter again and come up with a response to the complaints.

"But even without hearing the explanation, I'm still inclined to think the taxes should be coming down," said Supervisor Alan H. Magazine (D-Mason).