A county prosecutor said Friday he would not appeal dismissal of a first-degree

murder charge against Dr. Jack Kevorkian, whose "suicide machine" was used by an Alzheimer's patient to kill herself.The case against Kevorkian, a retired Royal Oak pathologist, was thrown out Thursday by Oakland County District Judge Gerald McNally. His ruling followed two days of testimony and the viewing of a dramatic videotape in which Janet Adkins, 54, told Kevorkian, "I don't want to go on."

Adkins, of Portland, Ore., died June 4, two days after the tape was made, in the back of Kevorkian's van in a remote park. She was hooked up to an intravenous device that permitted her to inject herself with a lethal solution.

McNally, calling suicide "a private and personal matter," held that Kevorkian committed no crime under state law and that the question of criminality in assisting suicide was an issue for the Legislature, not the courts, to decide.

Oakland County Prosecutor Richard Thompson said Friday he would not appeal the ruling and that it was time for the Michigan Legislature to eliminate confusion over assisting suicide.

He said he was not conceding it was legal but would not pursue further legal action against Kevorkian.

"I think this is a question pre-emi-nently for the legislative branch of government," Thompson said.

Michigan Gov.-elect John Engler, reacting to McNally's ruling, said he would push for legislation to outlaw helping a person commit suicide. He said he hoped the Legislature will act on a measure early in 1991.