Marie S. Nahikian, a candidate for the Democratic at-large seat on the D.C. City COuncil, charged yesterday the rival candidate Betty Ann Kane is not an efficient manager because she permitted a $40,000 overrun to occur in the Board of Education's postage budget. Kane denied the accusation.

In a news conference, Nahikian said Kane - who chairs the school board's finance committee - ignored a prediction of the overrun when it was made in a memorandim to the board last Feb. 24.

In that memo, Dwight S. Cropp, the board's executive secretary, said unspecified board members were send "mail-outs" to the community.

By failing to act on that early warning Nahikian contended. Kane showed negligence of her duties and cast doubt on her claims of being an effective financial overseer.

Nahikian released a copy of a second memo written by Cropp on Aug. 23 saying the predicted overrun had occurred, and that further large mailings must be halted until the board acts to replenish the postal fund.

The board's postal budget for the 1978 fiscal year is $45,779. The overrun would push actual spending above $85,000.

Kane, in her denial of Nahikian's charge, said the February memo from Cropp did not contain any request for a budgetary change. That request was not made until the Aug. 23 memo, which was officially referred to the finance committee last week, Kane said it will be dealt with at a meeting scheduled for Sept. 14.

Cropp, in a written statement yesterday, sided with Kane on the issue. School board president Conrad P. Smith, who said he supports Kane's council candidacy, called Nahikian's charge "pure nonsense."