Lindsey Scott, who received an honorable discharge from the U.S. Marine Corps this week, has applied to become a police officer in his home town of Louisville.

Scott, who was acquitted Feb. 19 after a second court-martial on charges of rape and attempted murder stemming from an April 1983 incident at Quantico Marine Base, is scheduled to take the police examination March 19, according to a department spokesman.

Scott has a degree in corrections from Eastern Kentucky University and was a military policeman in training to be a criminal investigator at the time of the assault on the wife of one of Scott's colleagues.

Scott was convicted in a 1983 court-martial, but the verdict was overturned last summer. The Marines then ordered a second trial, which began Jan. 25.

Sgt. Carl Yates, the Louisville police spokesman, said Scott's initial conviction will not be held against him. "It's only the final outcome of the case that we consider," Yates said.

Scott's experience in law enforcement in the Marines may give him a leg up in the department's rigorous application process, Yates said. "Usually people with a background in police work do better because of their background," he said. "Their aptitude seems to be stronger for this work."

Scott requested that he be discharged from the service almost immediately after he was found not guilty, and he received an honorable discharge on Monday. The Marines did not announce the action.

Under the terms of the discharge, Scott was promoted to sergeant, with back pay at that rank retroactive to Sept. 1, 1984. That was the date on which he would have been eligible for promotion to sergeant had he not been convicted in October 1983.

In that court-martial, Scott was found guilty on charges that he raped, sodomized, abducted and tried to kill the wife of a military policeman with whom he worked. He was sentenced to 30 years at hard labor, was demoted to private and was docked $500 a month for 36 months.

He served about four years in prison at the federal penitentiary at Fort Leavenworth, Kan. A Marine Corps spokesman at Quantico said Scott received $18,000 last summer in back pay that had been deducted over three years after his conviction.

The spokesman said he is not sure how much back pay Scott will receive from his retroactive promotion to sergeant.

Scott, who was moving into a new home in Louisville yesterday, could not be reached for comment. His wife, Lolita, said that Scott also had applied to the Louisville Fire Department for a job.

The Rev. Patrick D. Delahanty, a Louisville clergyman who raised money and support for Scott's defense, said Scott was recruited by the police and fire departments "totally out of the blue."

Scott became something of a celebrity in his home town as his case wound its way through the military justice system. After the original court-martial, a witness came forward who said she saw Scott shopping miles away from the Marine base at the exact time the victim said she was abducted.

Scott's conviction was upheld in 1986 by one appeals court on a split vote, then overturned unanimously last summer by the nation's highest military court, which ruled that the guilty verdict was tainted by the failure of Scott's original civilian attorney to prepare a competent defense.

In last month's verdict, four of the seven jurors voted to convict Scott. Under military rules, five votes were necessary for a conviction.