Downs' supervising officer, however, had "lost confidence" in him and asked that he be transferred, according to the memo. He subsequently was.
Downs - who will be paid $93,000 in his new role as a district watchdog - did not return several phone calls for comment.
As inspector general of the school district, he is charged with uncovering wrongdoing in the schools, including in the areas of contracts, workers' compensation and payroll.
Asked about the allegation and Downs' transfer, Philadelphia School District officials said they were not aware of that portion of Downs' past when the School Reform Commission approved his hiring last month.
"He had a very clean record. We thought he was infinitely qualified [for the job], with 30 years on the force and as a liaison to the school district," said Cecilia Cummings, a district spokeswoman.
Downs - a 33-year veteran of the Police Department - and a female officer under his command were discovered in Downs' unmarked police car at 1 a.m. on May 14, 1998, according to the memorandum. Both were off duty at the time, a source said.
Downs' car was parked in the 1200 block of South Juniper Street, an area within the Third District, of which Downs had command. According to the internal police report, Officer John Tittermary responded to a radio call about the auto.
Tittermary "shined his spotlight on the captain's car and [the female officer's] head popped up from the seat," according to the report. Downs drove away.
"Tittermary followed him to Broad and Christian Streets, where the captain got caught at the red light," according to the memorandum. Downs then told Tittermary everything was fine and drove off, the report said.