After a bureaucratic melodrama that rivaled the Perils of Pauline, an initiative on mandatory sentencing for those found guilty of violent and drug-related crimes was ordered onto the District of Columbia's Sept. 14 primary election ballot yesterday by the Board of Elections and Ethics.

A week ago, more than a month after the deadline for a final decision, the board reached a tentative finding that petitions seeking the initiative had fallen short of the 14,442 signatures, distributed appropriately among the city's voting wards, that were required. Yesterday, after a review by the measure's chief sponsor, the board agreed the goal had been met with 15,089 valid signatures.

Hailing the decision, council member John Ray (D-At Large), a candidate for mayor and chief backer of the initiative, voiced frustration at the process. Contending that a citizens' committee he heads found the board's staff had a 13 1/2 percent error rate in rejecting signatures, Ray declared:

"We had to fight the board all the way . . . we ourselves did all the work the board's staff was supposed to do. So we won. But no citizen or . . . committee should be required to overcome such obstacles . . . "