You must study each, but that does not mean you must devote the same amount of time to each.
You must first study the statute to know what the statute provides and to see how you construe the statute before you see whether your construction and application of the statute mirrors that of the appellate courts.
Then you need to spend most of your time reviewing the appellate court decisions (case law) to ensure that you correctly understand how the appellate courts construe and apply the statute, so that you can see whether your particular client and case are helped or hindered by both the statute and the appellate courts’ construction and interpretation and application of the law.
If all you did was study appellate case law, however, then you would be doing yourself and your client a disservice. If you don’t do that, then if all you do is take the appellate courts’ decisions as gospel, you may end up perpetuating and erroneous construction and application of a statute to your client’s/cause’s detriment. There are many instances in the past and there will be many instances to come where a sharp attorney realizes that the appellate courts have misconstrued and/or misapplied the statute. So you have to read the statute first and do your best to understand its meaning and application yourself.
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