Born in Malvern, Arkansas, Overton was subsequently educated at the University of Arkansas and its School of Law. Upon graduation in 1964, he went into private practice. In 1979, Overton was appointed to his District Court by President Jimmy Carter and was confirmed by the Senate on 10 May. Overton held this post until his death in 1987.

He 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. This statute was advocated by its supporters as providing equal treatment of creation science as the Theory of Evolution in the science classrooms.

When Judge 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. A theory that is by its own terms dogmatic, absolutist and never subject to revision is not a scientific theory.

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

1. It is guided by natural law;
2. It has to be explained by reference to natural law;
3. It is testable against the empirical world;
4. Its conclusions are tentative, i.e., are not necessarily the final word;
5. It is falsifiable.

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