Six girls who live and study and play together in Milford, Conn., and who just happen to be extraordinary gymnasts, won the team competition yesterday afternoon in the the first-annual Nation's Capital Cup gymnastics tournament.

The Connecticut Gymnastics Club totaled 187.10 points from performances on the balance beam, vault, uneven parallel bars and in floor exercises before almost 1,000 spectators at the University of Maryland's Cole Field House.

The Parkettes from Allentown, Pa., led by Joanne Beltz, the 1977 senior natinal champion, placed second with 184.90 points. The KIPS from Long Beach, Calif., with Donna Turnbow, the 1977 all-around club champion, were third with 181.95.

In individual competition last night, Shannon Coleman of the KIPS club was high-scorer on the balance beam, collecting 19.25 points. The judges gave Coleman a 9.65 for her evening performance, highlighted by some difficult splits and arabesques. The score was combined with her 9.7-point afternoon performance for the final score.

Linda Kardos of the Gym-Dandies of Washington, Pa., and Jodi Kline of the Parkettes tied with 19.3 points each in the vault.

Because Kardos' point total in all events for the day were 37.15 and Kline's 37.06. Kardos was declared individual winner in the vault under international tie-breaking rules.

Coleman picked up an even more prestigious award later in the night when she was named best all-around gymnast of the tournament on the strength of her 9.55 average score for all four events.

Besides winning the beam, she tied for first place in floor exercises with Linda Tardiff of the Connecticut club. Each had 19.05 points.

In the uneven bars, Connecticut's Marcia Frederick earned 9.8 points in both the preliminary and the individual finals to take the event with 19.6 total points.

Ma Va Teens from Rockville, the only local independent club entered after a dispute over Stephanie Willim's absence prompted the ouster of the Silver Spring M.G.'s club, placed sixth with 177.50.

The University of Maryland's women's gymnastics team, a last-minute replacement for the M.G.'s, finished eighth with 157.45 points.

The Connecticut club is directed by Muriel Grossfield, a three-time U.S. Olympian and coach of two U.S. Olympic teams. Grossfield was pleased that the nation's top female gymnasts had this opportunity for head-on competition.

"All the gymnasts here have reason to believe they can qualify for the U.S. Olympic team," Grossfeld said. "Our kids compete primarily in U.S. Gymnastics Federation open meets. Most of the competition is individual, so we were very, very happy to have the team competition.

"The elite kids need more opportunities to compete, but we in the United States don't have as many good coaches and training centers as we should have." Grossfield comtinued.

"We haven't trained as much as we should have. We're on the opposite side of the ocean from the countries we should be competing with to prepare for the Olympics, too."

Grossfled said she believes the U.S. should place at least third in next year's International Gymnastics Federation World Championships.

"We're definitely good enough for that. The Soviet Union is in a class by itself, but our chances should be limitless, with the exception of first place," Grossfeld said.

The same goes for the 1980 Olympics in Moscow, she said, where the U.S. women's team "can definitely be third and should try for second."

Grossfeld said she bases her opinion on the fact that younger and younger girls are taking up gymnastics, allowing more training time, and to the improvement in gymnastics equipment.

Grossfeld's young gymnasts live together, with house parents, next door to the gym. They go to school together and are excused early so they can practice a few hours at the gym before studies.