Three persons, including a Treasury Department employe, have been indicted on mail fraud and other charges for allegedly obtaining unemployment compensation from the District of Columbia while they were employed full time by the federal government.

The indictments, made public yesterday, charged Donnie J. Johnson, who works in the department's Bureau of Government Financial Operations, and former Treasury employes Billy Joe Wright and Shirley R. Anderson. Anderson also formerly worked for the D.C. Officer of Personnel.

Prosecutors said the payments to the three were uncovered by "Operation Cross Match," an ongoing program that cross-checks the Social Security numbers of those receiving unemployment benefits with those of government employes.

A spokesman for the U.S. attorney's office said a total of 40 cases stemming from Operation Cross Match have been referred for prosecution in the past year.

According to the indictments, Wright, 39, of 1439 Kennedy St. NE, received $4,536 in unemployment benefits from June through early December 1982. The indictments state that Anderson, 34, of Danville, Va., received $3,608 from Sept. 25, 1982, through Feb. 26, 1983.

Johnson, 38, of 3332 Curtis Dr., Hillcrest Heights, was charged with receiving $5,448 in unemployment benefits to which he was not entitled from Sept. 26, 1981, through April 3, 1982.

Prosecutors said all three had been receiving unemployment benefits legitimately but failed to notify authorities when they got new employment.

A law enforcement official said Anderson was convicted of embezzlement and welfare fraud last year in Virginia.