A 26-year-old tenant, who was raped in her apartment near Dupont Circle, has received an $137,500 out-of-court settlement of a lawsuit in which she accused her landlord of failing to maintain adequate security in the building.

The settlement, believed to be the largest ever of its kind in the city, was reached last week on the day the victim's $1.5 million lawsuit was scheduled for trial in the D.C. Superior Court.

In her suit, the woman charged that real estate investor Matthew M. Mezzanotte, who with his wife owns the Granite State Apartments, 1731 New Hampshire Ave. NW, failed to maintain workable locks on the building's entry doors and refused to install chains and peep holes on the doors of individual apartments that would have provided greater security.

Because of these conditions, the woman said she was raped by a man who made his way into the building, knocked on her door and -- when she answered -- forced his way into her fourth-floor apartment.

At the time of the incident, June 21, 1979, the building owner had notified tenants of plans to conver the structure into a hotel and was doing all he could to get tenants to vacate, according to documents filed in connection with the case.

Neither Mezzanotte nor his attorney could be reached for comment yesterday.

The settlement is one of a series around the country in recent years in which victims of crimes have received compensation from those judged responsible for the victimization. In one of the most notable cases, singer Connie Francis received a $1.45 million settlement from a motel chain after she was raped in a Long Island motel. She charged the room lock was inadequate.

In the latest Washington case, the rape victim's attorney, Michael S. Levy, said Mezzanotte's insurance company recommended the settlement rather than going to trial. He said the company's payment, tax-free to the victim, was made this week.

The victim, who asked that her name not be published, said she suffered severe emotional reactions for months after the rape, including sleepless nights, a recurring fear that she had contacted veneral disease and an inability to earn a living. A graduate of a midwestern college, she did secretarial work and hoped to become a free-lance writer.