State Capitol Buildings without a Dome

South Dakota's capitol in Pierre does have a dome.

You mixed up the Dakotas. Bismarck’s capitol does not have a dome, while Pierre’s does. Have been to both, so I speak from experience.

The capitol building in Lincoln, Nebraska has a tower which looks like it’s crowned with an external dome. This likely doesn’t count as an example.

Also, the capitol building in Salem, Oregon doesn’t have a rounded external dome. It likely counts as an example.

While Delaware’s capitol has a small rounded fixture near the top of its church style spire, it’s usually included in lists of dome-less capitols. It’s definitely smaller than the one on Nebraska’s capitol building.

It likely counts as another example to add here.