The administrator and co-owner of a Prince George's County nursing home was indicted here today on 10 counts of Medicaid fraud, theft and false pretenses.

Dr. William Greco became the fourth person charged in connection with a long-running investigation into the financial affairs of the Magnolia Gardens Nursing Home and the adjoining Prince George's Doctors Hospital in Lanham. The grand jury, according to court papers filed in connection with subpoenas, also is investigating Dr. Leon R. Levitsky, a politically prominent Prince George's Democrat and Greco's partner in both ventures.

Today's vaguely worded indictment charged Greco with falsifying Medicaid reimbursement reports for the nursing home for the years 1977 through 1979 and obtaining state monies to which he was not entitled.

No amount was specified in the indictment. Assistant Attorney General Stefan D. Cassella said, however, that the allegations stemmed from improvements made to Greco's home in 1977, the cost of which were charged to the nursing home.

Greco could not be reached. "As you might imagine, we don't have any comment at this time," said Thomas Morrow, one of his attorneys.

Two other figures connected with the nursing home have entered guilty pleas, including the contractor who worked on Greco's home and a former nursing home bookkeeper who said in an affidavit that Greco had instructed her to pay for the home improvements. A third person connected with the hospital has been indicted for income tax evasion.

Robert Gonder, a grand jury witness and the hospital's vice president for finances, was killed on April 2 when the car that he was driving struck a tree in Montgomery County. His death came a day after his Potomac home had burned in a fire that was determined to be arson. Police said that Gonder had been a suspect in the fire and last week officially ruled his death a suicide.

Cassella said the state Medicaid investigation that began in 1980 has been prolonged by a team of defense lawyers who have fought nearly all efforts to subpoena documents and witnesses. About a dozen rulings arising from the proceedings have wound up in the state appellate courts, where the prosecutors have prevailed in most instances.

Earlier this week the Maryland Court of Appeals upheld the state attorney general's power to investigate Medicaid fraud using a Baltimore grand jury. Defense lawyers had argued that Prince George's County was the proper place for such an investigation. The state Medicaid office is in Baltimore.

But the court threw out the subpoena in the case, since the term of the grand jury that issued it had expired. Cassella said that he intends to obtain another subpoena from the new grand jury, whose term begins on Monday.