Prince George's Democrats will choose a new senator Tuesday to represent the 24th legislative district, but the specter of Tommie Broadwater Jr.--stripped of the seat after being sentenced to six months in jail for food stamp fraud--haunts the selection process.

Broadwater, who was the county's only black state senator and is one of Maryland's leading politicians, supports District Court Judge Sylvania W. Woods as his successor among the dozen persons vying for the post. Woods, whose 1976 appointment to the bench was backed by Broadwater, is the father of a 24th district state delegate.

"Judge Woods would be the best," Broadwater said last week. "He's the most knowledgeable, he's well known. . . . He's acceptable by everybody, because we as a unit and we as a team could work together as we have in the past."

Broadwater's support, however, is only one of the elements expected to come into play this week as factions in the Democratic party and the black community struggle to fill the void left by his removal from the legislature.

"It's wild," said central commitee chairman Gary Alexander, "It's sort of like that old Abbott and Costello routine, where they start off and say 'Who's on first?' Any time I run into anybody, it's 'who's on first?' It's been a continuing, day-by-day changing picture."

Several political activists have suggested that Broadwater and Woods have agreed that Woods would serve as a puppet legislator with Broadwater continuing to pull the political strings. Observers speculate that Woods would step aside if Broadwater decides to run for the Senate seat in 1986.

Because Broadwater loses his right to vote while serving his four years probation, he would not be able to run as a Democrat or Republican in 1986. However, according to the attorney general, Broadwater could run an independent campaign.

Broadwater has angrily denied that any deal has been made. But, he said, "There's no question that I would like whoever wins to step aside if I run in 1986."

Woods could not be reached for comment.

At least three other candidates are still active players in the "who's-on-first?" competition.

Orphans Court Judge Decatur Trotter, a former delegate who ran a losing race for Broadwater's Senate seat in 1978, is one of those.

Because he believes that as a sitting judge he is barred from political involvement, Trotter has avoided any public statement of his candidacy. He said last week that he would decide over the weekend whether to resign his post to appear at the central committee's meeting Tuesday.

Trotter has the backing of county council member Floyd Wilson, and several state senators reportedly are leaning toward supporting Trotter, largely because of his experience in the General Assembly.

But Sen. Thomas V. (Mike) Miller, who has indicated support for Trotter, said that Woods, or school board member Bonnie Johns, would also be acceptable to him.

Johns, the leading choice of the Black Democratic Council, also has the support of council member Hilda Pemberton.

County teachers, however, have thrown their support behind Central Commitee member Carolyn J.B. Howard, a school principal. She was endorsed last week by directors of the Prince George's County Educators' Association, in part because the teachers' union is angry about Johns' stand against binding arbitration of grievances, a major goal of the union in its continuing contract negotiations with the board.

"We wanted to go on record that we think she Howard is the best candidate," said union president Paul Pinsky, "and because we have doubts about at least one of the candidates."

Other announced candidates are Lillian Lewis and Fred Prince, both unsuccessful former candidates for various county offices.

Policital observers say the selection of a successor to Broadwater is a referendum on a number of conflicts within the county's Democratic party. They say these include the willingness of male politicians to appoint women to major posts and the extent to which state senators, long considered the major force behind legislative appointments, still control the process.

And members of the black community say they are watching closely to see whether their new leader will be someone controlled by the Democratic establishment, or an independent voice for their concerns.

As political maneuvering and sometimes heated debate continued last week, members of the central committee insisted that the outcome will remain uncertain until they convene on Tuesday night.

"All I know," said central commitee member Jeanette Gordy, "is I'm going to pack my lunch and be there Tuesday."