Jury selection is expected to begin in U.S. District Court today in the trial of Mary Treadwell, the only remaining defendant in the conspiracy and fraud case against former officials of a Youth Pride Inc. real estate spinoff company.

Treadwell, three other officers of the company, P.I. Properties, and an accountant were indicted by a federal grand jury 15 months ago--after a 2 1/2-year investigation into allegations that they used P.I. Properties to defraud the government and low-income tenants of thousands of dollars which they used for personal expenses and to finance private, profit-making ventures.

The grand jury investigation followed a 14-month investigation by The Washington Post into complaints about Treadwell's operations, including some from tenants at Clifton Terrace, a dilapidated low-income apartment project in Northwest Washington managed by P.I. Properties. The tenants complained that they were without heat, electricity, water and sanitary living conditions.

Tenants at two other low-income projects managed by P.I. Properties had similar complaints. Federal funds to P.I. Properties were cut off shortly after The Post published a series of articles on the projects and Youth Pride shut down last August.

In past interviews with Post reporters, Treadwell acknowledged "some things I would judge as mistakes," but "not theft." She has steadfastly maintained innocence of wrongdoing.

Since the grand jury indictment in February 1982, prosecutors dropped charges against one official, Arlington political leader and minister Charles W. Rinker Jr., after Rinker passed a polygraph examination.

Prosecutors also have accepted guilty pleas from three others. Accountant Ronald S. Williams, Treadwell's former husband, pleaded guilty in April 1982 to charges of giving false statements to prosecutors. He was fined $5,000 and placed on three years' probation.

Robert E. Lee, former general manager of P.I. Properties, pleaded guilty last January to conspiracy and making false statements to federal officials. Lee faces a maximum 10 years in prison and $20,000 in fines.

Treadwell's sister, Joan M. Booth, another key official in P.I. Properties, pleaded guilty last October to conspiracy and one count of tax evasion. Booth, who faces up to five years in prison and a $10,000 fine on each charge, has not been sentenced.

In addition, Johnny Mickens III, Youth Pride's former chief financial officer, who was not named in the indictment, pleaded guilty to failure to file income taxes in a separate case. He was sentenced to three years' probation.

Williams, Mickens and Lee have all agreed to testify for the government, but prosecutors, who say they expect to call 65 to 70 witnesses in the case, declined to say whether they will call any or all three as witnesses during the trial, which is expected to last about six weeks.

Both sides have told U.S. District Court Judge John Garrett Penn that they expect selection of 12 jurors and six alternates to take all week. The jury selection is expected to be laborious in part because of the publicity that has surrounded the case.

In addition to the government witnesses and hundreds of documents that will be used by both sides in the case, Treadwell's attorney, John W. Nields, has said that he expects to call 30 witnesses to show that Treadwell is not guilty of charges of conspiracy, fraud, tax evasion and making false statements to federal officials.

Penn appointed Nields, a partner in the Washington law firm of Howrey & Simon and a former government special prosecutor, to represent Treadwell after she said last year that she had outstanding debts totaling more than $60,000 and could not afford to hire a lawyer.

At a hearing last week, prosecutors told Penn that Treadwell, who had offered to take a polygraph examination, had been offered the examination but declined to take it.

Nields told Penn that Treadwell did not refuse to take such a test but only objected to the way in which prosecutors had offered to conduct it.