Leopold S. Senghor, the scholarly and courtly president of the Republic of Senegal, is scheduled to arrive in Washington today for a three-day visit, during which he will formally establish "sister city" ties between the District of Columbia and Dakar, the Senegalese capital.

Senghor will meet briefly with President Carter and Secretary of State Cyrus Vance. However, a State Department spokesman described those meetings as courtesy calls. "No serious bilateral issues" between the two countries will be discussed, the spokesman said.

The main purposes of Senghor's visit, Sengalese Embassy officials said, are to reciprocate Mayor Marion Barry's visit to Senegal during Barry's 21-day swing through five African countries last year and to preside over closing ceremonies Sunday for an exhibit of Senegalese art at the Corcoran Art Gallery.

Arrangements for the visit are being handled by the mayor's office, which has been taxed by the logistical problems of hosting a head of state at a time when the city is facing a potential budget deficit of $172.4 million.

For example, arrangements for an official dinner scheduled for Monday night at the Shoreham Hotel were left open until the last minute while officials waited to see how fast the contributons they requested from the business community would come in.

Senghor, 73, is a poet and easayist, a recognized scholar and one of the most durable and respected African leaders.

He has held power in Senegal since it became independent from France in 1958. In 1964 he banned all opposition political parties, but he gradually allowed them to return and was reelected most recently in 1978 in multi-party elections.

Educated at the University of Paris, Senghor speaks six languages and was a close friend of the late French president Georges Pompidou. He has published seven collections of poetry as well as numerous political and philosophical essays.

Senegal is a developing nation on the west coast of Africa about the size of South Dakota. The country has undergone limited industrialization, but its economy remains primarily agricultural with peanuts being the principal crop.

While in Washington, Senghor will also meet with Robert S. McNamara, head of the World Bank, which provides economic assistance to developing nations.

While Barry was in Africa last year, Senghor asked his assistance in finding a site for the exhibit of paintings, tapestries and drawings. A number of Washington galleries had turned the exhibit down, claiming they could not schedule it.

Barry said he hoped the "sister city" relationship would foster technological and cultural exchanges between Washington and Dakar, and said he hoped local businesses might find fresh markets in the Senegalese capital.

Barry's Africa trip received some criticism because of uncertainty over what concrete benefits it could bring the District.

Senghor is scheduled to arrive at Andrews Air Force Base at 4 p.m. today. On Sunday, he will tour the East Wing of the National Gallery of Art at 10:30 a.m., then attend an 11:30 Easter mass -- celebrated in French -- at the Howard University Law School chapel at 2900 Van Ness St. NW.

That afternoon, beginning at 3 p.m., Senghor will attend the closing of the art exhibit.

On Monday, he will visit Ballou High School, 4th and Trenton streets SE to view the school's highly regarded science and math facilities. The school will be closed for Easter break, but Senghor is scheduled to meet with selected students.

Later that day, he will meet with Vance and McNamara. Monday evening, Barry will host the formal dinner for Senghor and 100 invited guests, including diplomats, While House staff members, members of Congress and a few high-ranking city officials.

Dwight S. Cropp, the mayor's executive secretary, said the dinner would cost "between $2,500 and $3,000," all of which he said would come from private contributions.

Senghor will meet with Carter at the While House at 9:00 a.m. Tuesday. The Senegalese president is scheduled to leave Andrews Air Force base for Senegal at 11 a.m.