Can a civil engineer build a small building without an architect?

At least where I practice, California, civil engineers can design any type of building expect for hospitals. But, just like architects, while they are allowed to design these their design will be questioned with a mind that this is allowable but unusual behavior for that license.

As an architect, I face similar problems when I supply my own structural design and calculations. Very few architects do that on projects more complex than a house, but if you are competent in your engineering most jurisdictions will allow you to proceed.