The U.S. Supreme Court refused yesterday to review a lower court decision permitting the development of the Pentagon City office, apartment and commercial complex across Shirley Highway from the Pentagon in Arlington.

The court's decision clears the way for construction of the $31 million development. A group of residents near the 118-acre tract, calling themselves the Pentagon City Coordinating Committee, contended in a lawsuit that the development would increase noise and air pollution and worsen traffic congestion in the area.

The committee said that the Arlington County Board's approval of the development nearly two years ago was "unreasonable, arbitrary and capricious."

But Arlington Circuit Court Judge Paul D. Brown dismissed that claim and ruled in December 1976 that the committee had failed to prove "in terms of dollars that their special property interests will be harmfully affected by the increased traffic," which they said the complex would bring.

Last July the Virginia Supreme Court upheld Brown's decision, saying that there was "no reversible error," in the lower court's ruling.

"I think that's the end to that particular litigation," John H. Quinn Jr., a committee member, said yesterday. Quinn said the committee will explore the possibility of filing suit under the Virginia clean air act or the U.S. clean air act, "both of which," he said, "may be violated" by the development.

According to William B. Lawson, an attorney for the developers, construction already has begun and the first phase of the complex may be completed by 1980.

The first phase is to include a nursing home, some subsidized housing for the elderly and some low-rise family housing.

When completed in 1990 the development will include 2,000 hotel rooms, 1.2 million square feet of office space, 800,000 square feet for commercial use, about 7,150 apartments, and 13.5 acres of parkland. A completed Metro station is one feature of the site.