The talk of the Prince George's County Courthouse, a stately structure that dominates Upper Marlboro's Main Street, has been the quiet electioneering of late staged by a boyish Circuit Court judge and his former boss, the hard-nosed county prosecutor.

Unlike most elections, the appeal is not to many voters, but only one -- Sen. Paul Sarbanes (D-Md.). The reason is simple. Sarbanes holds the only ballot.

The two candidates -- Circuit Court Judge Howard S. Chasanow and State's Attorney Arthur A. (Bud) Marshall -- would like to fill the vacant judgeship on the U.S. District Court of Maryland.

Sarbanes makes the final recommendation to President Carter, who makes the appointment.

There are many other lawyers around the state interested in the prestigious lifetime post and for many reasons the chance that Chasanow or Marshall will be chosen probably is remote. There has never been a Prince George's representative on the District Court in its 191-year history. Sarbanes' ties are with high-priced, old-time law firms in Baltimore, and President Carter has shown interest in appointing women or minorities to such positions.

Yet both men are gambling on the possibility Sarbanes -- who faces reelection in 1982 -- might recommend a Prince Georgian to appease county Democrats who feel he has slighted them.

The two have been campagining with remarkably different styles. The 43-year-old Chasanow, who has a reputation for large measures of both brilliance and ambition, has conducted his campaign quietly. Judicial ethics preclude his openly soliciting support or appearing, as Marshall has, at political functions.

For example, Chasanow recently was seen padding around Ocean City at a state bar association convention just letting people know that he was interested in the judgeship. If they felt like telling Sarbanes that Chasanow was a fine candidate, that was okay with him, the Circuit Court judge told people, knowing full well that most lawyers have a latent tendency toward compulsive letter writing.

In addition, Chasanow garnered more than 300 votes as "highly qualified" in a recent county bar association poll, the results of which are forwarded to Sarbanes.

However, the bar vote was a beauty contest made even more meaningless by the fact that Marshall, apparently deciding to solicit support in a different manner, was not on the ballot.

Marshall has won the endorsement of many local politicians and has sent out letters to county lawyers asking them to "communicate directly with Senator Sarbanes, if they support his candidacy.

The letter raised some eyebrows since it was written on official state's attorney office stationary. But it is the power behind Marshall's office and his widespread appeal in Prince George's that make him such an attractive candidate in terms of Sarbanes' political needs.

"If anyone thinks this selection will be based on the judicial qualifications of these men," said one longtime observer of the county scene, "they're completely wrong. Sarbanes will say: 'Besides the fact that you can read and write, what can you do for me?' Marshall has an office of 100 people and Chasanow has one secretary and a clerk."

It is being a sitting judge seeking another judgeship that makes Chasanow's efforts so difficult.

Recently, he discouraged several lawyer friends from starting a phone campaign to Sarbanes, and Chasanow has avoided political functions which might give the appearance of judicial impropriety.

For example, while Chasanow rubbed elbows with the big wigs in Ocean City, Marshall was introducing Sarbanes to a local gathering of Democrats in Brandywine.

"Bud Marshall has been a faithful loyal member of the team," one local politician remarked later. "He ought to be our man."

Meanwhile, Chasanow frets about his judicial feebleness when it comes to angling for the job. "My theory," Chasanow said recently, "is that the best thing I can do is nothing -- I don't want to make a mistake."

A spokesman for Sen. Sarbanes' office would not comment on the selection last week, but Marshall and Chasanow have interviewed with Sarbanes and expect his announcement soon.