The woman, a Catholic who lived near Dungannon, Co Tyrone, died when loyalist gunmen fired through the window of a bungalow.
Their victim, Roseanne Mallon, was staying with her sister-in-law, who had left the room to answer a telephone call when the attack came. Hers was the 23rd violent death in the province this year.
The RUC said three men had been arrested. Police sources indicated they believed a notorious loyalist gunman, known in the media as 'King Rat', was involved in the killing.
The illegal Ulster Volunteer Force, with which 'King Rat' is associated, has been responsible for more than 30 killings in Tyrone and Armagh since 1990.
Miss Mallon's death gave rise to another collusion controversy, with Sinn Fein and a family member claiming that collusion between the security forces and the killers had played a part in the attack.
Sinn Fein claimed that on Saturday night two youths had discovered guns in a derelict house near by, and had been threatened by a number of men in combat dress. But the RUC said a man who had been shooting rabbits in woodland while wearing camouflage dress had come forward voluntarily and made a statement which had satisfied them.Reuse content