This is the correct answer. And if I recall from law school, the only state that did otherwise was Louisiana and most legal scholars note that the state is kind of an aberration from the rest of the country based on its Napoleonic roots. Napoleon was kind of a weird bureaucratic dictator and liked all laws to be explicitly spelled out in writing; I believe (though I don’t know because I haven’t really researched it) that his code basically disposed with “common law” altogether.

The rest of the US is based on the English common law tradition, where “the law” is a mix of statutes and court precedents. Most states have passed new statutes to cover most situations but still depend on case law to flesh out ambiguities in the statutes, which is basically why courts require trained specialists as lawyers and judges.