Legal Question in Intellectual Property in Louisiana

I don't want to sound crass, but your question is sort of like asking, "I own a car, do I need a bicycle?" Both are modes of transportation (just like copyrights and patents are both forms of so-called "intellectual property"), but beyond that, they don't have much to do with each other.

Pretty much anyone who has done a finger-painting in preschool owns a copyright. It's automatic, once the work of authorship is fixed in a tangible medium of expression. But of the billions of copyright holders, few need patents, and if they do, it is generally for things unrelated to their copyrights.

This answer, for example, is copyrighted. I don't need or want a patent for it. (I don't really even want a copyright for it.)