Seated on a piano stool with her feet dangling six inches off the floor, 9-year-old Jennifer Somers dazzled listeners at St. Patrick's Church, 1655 Foxhall Rd. NW, last Saturday afternoon. After playing several pieces on a miniature violin, she finished a memorable 45-minute performance by singing, unaccompanied, "How Much Is That Doggy in the Window" and "My Favorite Things."

Jennifer was one of the stars of the Levine School's Play-a-thon, a musical marathon to raise money so that the school, which uses St. Patrick's evenings and Saturdays, can have a building of its own.

An opening session of the Play-a-thon was held at the District Building earlier in the day. Mayor Marion Barry, who had proclaimed the day "Levine School of Music Day" did not appear, and the weather was uncooperative, but undaunted Levine students went on with the concert.

Chucky Reed, 14, with his four siblings, including 3-year-old Jason, made it sound like Sunday morning in City Council Chambers as they belted out gospel songs, "Soon Now Very Soon," and "I'm Glad," followed by a percussion trio and a flute trio performing Baroque dance tunes.

While more than 200 students kept the music going for eight hours here to earn donations pledged for their building fund, audiences in other cities also heard musical pleas for support: Levine School piano instructor Pierre Fournier entertained for an hour in a Martinsburg, W. Va., restaurant; his student Lorna Grenadier held a Play-a-thon party in New Orleans; and violinist Anthony Hopkins performed at Detroit's Children's Heritage Museum.

The school, named for amateur musician and Washington attorney Selma Levine, was founded by three of her friends in the spring of 1976, about a year after her death. Founder Jaclin Marlin said she, Ruth Cogen and Diana Engel "wanted to name it after Selma in memoriam; she had been a true lover of music." Marlin said the idea of the school came out of "our cocktail party conversation. We were always saying, 'What this city needs is a really good music school.' "

The Levine School has become a victim of its own success. When it began seven years ago with 40 students, there seemed to be plenty of room in its first home, the Reorganized Church of the Latter Day Saints on Massachusetts Avenue NW. But it quickly outgrew that location and moved four years ago to St. Patrick's.

Now, with 400 students and 40 teachers, enrollment has halted. "We just don't have any room to grow," said administrative assistant Diana Hartwick Young. "We've got lessons in every nook and cranny of this building, and we now have a waiting list of students that we just can't find the space for."

The school's fundraising goal is $1.7 million--the price of a building it has contracted to buy at 3615 Wisconsin Ave. NW. To get the building for that price, however, the school must pay the full purchase price by December, 1986. An initial payment of $600,000 is required by June to secure the purchase. Although the school is accustomed to raising funds with events ranging from bagel sales to benefit concerts, officials recognize that the building fund campaign is a big challenge.

"Our teachers are paid top salaries so that we can attract and maintain the best in the business," said public relations assistant Michael Mendelson. "Then, we have to provide scholarships for our students who can't afford to pay the full rate. But, despite the odds, we are determined to buy a building of our own."

The faculty includes 10 members of the National Symphony Orchestra, all absent from Saturday's festivities because the orchestra is on tour in Japan. Nine other teachers play with the Kennedy Center Opera House Orchestra. Sixteen are also college teachers.

"We needed to find a way to raise money, but also to involve everyone in the fundraising process," said Mendelson. He said that when he and the school's director Joanne Hoover thought of the Play-a-thon "we didn't expect to raise a lot of money from it, but we were looking for a consolidation of the efforts of everyone in the school in the fundraising process."

Saturday, while Jennifer Somers and other Levine School students entertained the audience in St. Patrick's upstairs auditorium, scores of other young musicians were waiting in corridors or tuning up to perform in other parts of the church's rambling building.

Downstairs in the conference room, violinist Kelly Kalibat performed variations on "Twinkle, Twinkle, Little Star," and in the choir practice room Lisa Brewer played a 10-minute Mozart piano concerto.

"We are determined to build a permanent musical institution in Washington," Mendelson said. "Washington had no real musical establishments before the Kennedy Center came into being, and there is no conservatory for musical studies. We hope that one day we will be Washington's 'conservatory.'"

"Our goals may not have been realized through the Play-a-thon," said school director Hoover, "but one thing is perfectly clear. The school must have a home of its own. If we can't come up with the money by June, we'll just look for another building. The momentum is there, so if the plans we so carefully executed don't work out, we'll just keep on going until we find a space we can call our own."