CBS has one of the flattest, dinner-plate root systems of any tree that I've seen. After windstorms there are almost no sinker or anchor roots.
Tap roots are only found on a few trees. They're generally in places where there are deep water sources.
A true tap root becomes a sinker or anchor root soon after the tree is established. Think of this...after a storm or lot clearing, how many 'carrots' have you seen coming out of the bottom of root balls? More common are a gob of roots but not a single root.