The trustees of Antioch University voted yesterday to end financial support for Antioch's innovative 13-year-old law school in Washington and authorized the university president to take steps to close the school unless it obtains major new backing soon.

The law school has been troubled for years by inadequate financing and facilities and recently has been beset by declining enrollment and threats to its accreditation by the American Bar Association. The trustees said they want to concentrate their efforts on rebuilding Antioch's main campus in Yellow Springs, Ohio, which has had its own serious financial and enrollment problems, and can no longer aid the school in Washington.

Alan E. Guskin, the president of Antioch, said yesterday that the law school will have until late November to find adequate new space and financing from supporters in Washington. The school's classrooms and library have been criticized by ABA evaluators.

Guskin said the law school's local governing board might find "another group or institution that could run it in a proper way." He said that "very preliminary" negotiations between officials of the law school and the University of the District of Columbia ended last summer.

"If the Washington community can support the law school, we'd love to see it continue," said Guskin, who became Antioch's president Sept. 1, "but a small midwestern university can no longer afford to foot the bill."

C. Norman Poirier, chairman of the law school's board of governors, said late yesterday that he was disappointed by the trustees' decision and thought Guskin's timetable for finding new facilities and support was "too tight."

"I'm reluctant to predict now what we'll do," he added, saying the board would probably meet late this week "to assess the situation."

Founded as an alternative to traditional law schools, Antioch operates as a public-interest law firm, requiring students to earn about a third of credits by handling cases for low-income clients. Its founders, Edgar and Jean Cahn, had operated a similar program at George Washington University, which was dropped by the faculty there.

The law school has frequently been marked by conflicts between its faculty, students and administrators. But these differences have subsided recently as the ABA has threatened to remove the school's accreditation after an inspection report said the Antioch's academic program was of "limited rigor" and its funding "inadequate."

The accreditation issue is on the agenda of two ABA bodies in November and December, though Antioch Law officials have expressed optimism that the school has satisfied the criticisms in accreditation committee reports.

Guskin said Antioch University has spent $4 million to subsidize the law school since it opened in 1972 but that it has been unable to raise enough funds to provide adequate space, competitive faculty salaries and scholarships.

He said the university's primary interest now is in rebuilding its main campus, where the enrollment has dwindled over the past decade from nearly 2,000 students to about 500.

The law school had recently arranged to lease the old Perry Elementary School at First and M streets NW for 20 years from the D.C. government but needed $2.5 million for renovations, said Poirier. But the trustees, who met Friday and yesterday in Yellow Springs, turned down the plan because they did not want to invest so much in a building they would not own.

Poirier said the law school's local board agreed with the ABA that the current classroom building at 2633 16th St. NW and its library three blocks away at 1624 Crescent Place NW were inadquate.

The library is rented for $1 a year from the Eugene and Agnes Meyer Foundation, which has asked the school to leave by next summer.

The law school now enrolls 382 students in its regular degree program -- down from 412 a year ago and 477 in the fall of 1983.