[1] Overton was nominated to the United States District Court for the Eastern District of Arkansas by President Jimmy Carter on March 7, 1979, to a new seat created by 92 Stat.

Overton continued to serve on that court until his death of cancer on July 14, 1987, at his home.

[2][1] Overton is known for his ruling on Act 590 "The Arkansas' Balanced Treatment Act" in McLean v. Arkansas, which was a law seeking to require the teaching of Creation Science in classrooms.

When Overton struck down the Act in 1982, he used the criteria that a scientific theory must be tentative and always subject to revision or abandonment in light of the facts that are inconsistent with, or falsify, the theory.

In summary, he held that a scientific theory to be taught in schools must have the following properties: