It depends on what you mean by "a murder." Do you know if charges were ever filed? If so you just need to go to the clerk's office where charges were filed. You will need at the least, the defendant's name. Depending on what happened with the case they may have retained the file or it may have been destroyed. If there was a conviction than they should definitely have a file on it with the judgment and charging instrument. Go there in person or call and have them mail the documentation to you. There will be a fee for this of course.
If no charges were ever filed than there might not exist any public record of the murder anymore. The only definite record would be the casefile with the police, but that is not a public record and there is no way to petition to see it if you have no direct connection to the case. Other than that you'd just have to find someone or some service that archived any newspaper articles on it. Unless you can find any books on the subject, that's about all there is unless you can track down someone old enough to remember facts about it.