A Prince George's County elementary school closed because of declining enrollments may soon be refilled with Anne Arundel County students who live five miles away in an area where schools are overcrowded.

Busing across county lines has never before been tried in Maryland, according to school officials, and raises a number of legal and political problems.

Prince George's school board president Norman M. Saunders said, "I would be in favor of the proposal if the school were operated by the Prince George's board, with a Prince George's program and Anne Arundel paid the full tuition rate for each student sent there. But we cannot have an Anne Arundel program in the Prince George's County school system."

Prince George's school board attorney Paul M. Nussbaum said that the proposed transfer would probably require the approval of the state superintendent of schools, and possibly even action by the state legislature.

Nevertheless, a consultant has recommended that the Anne Arundel school board rent or borrow Somerset Elementary School in Bowie and educate between 340 and 380 students there. Somerset was one of nine schools shut down by Prince George's in June 1977 because they were below 80 percent capacity.

At the same time, schools in the booming community of Crofton just over the Anne Arundel County line from Bowie are severely overcrowded. School officials in both counties believe that many families have been drawn to Crofton by prospect of lower taxes and the absence of the widespread busing for racial desegregation that exists in Prince George's.

Although Prince George's school officials have not yet been contacted by Anne Arundel about the plan, several said this week that they thought the cross-county line busing would be a logical use of the school building, which has been vacant since last June and has become a teen-age hangout.

"It's been horrendous the past year," said Bowie Mayor Audrey Scott. "The entire parking lot there is full of broken beer bottles, there are disturbances on weekends, and this is in a residential area where people are getting upset."

Somerset Elementary was opened in October 1962 on Somerset Lane, a quiet residential street in Bowie. A kindergarten addition in 1969 gave the school 22 rooms and a capacity of 570 students, according to Prince George's figures.

The school was closed after enrollment dropped to 339 in September 1976 and a study projected enrollment for September 1977 at 295.

Prince George's officials used the school building as a special education center during the 1977-78 school year, but shut down its operations completely after the special education program was moved to a new facility in Mitchellville.

Although Bowie officials have been negotiating with the county housing authority in the hope of arranging for the use of Somerset by a senior citizens group, Scott said yesterday that Anne Arundel's plan would be "an acceptable use for the school."

"It's a good idea," said A. James Golato, who represents the Bowie area on the school board. "It's an efficient use of the building and an efficient use of money. After all, it's not a foreign country that's across our border line."

Despite several problems with the idea, Nussbaum and school officials said the school could still be rented to Anne Arundel if both counties favored the plan. "If everyone wants to do it, I don't think the lawyers will ultimately stand in the way," Nussbaum said.