[PAR35]

It is the oldest in the US AND, the only one without a dome.

No. There used to be about a dozen without domes. Oklahoma recently added a dome; a quick search indicates conflicting info as to whether the current number is 10 or 11.

Louisiana is one.

A 'for what it's worth' Wikipedia entry said that there are 13, Virginia, Alaska, Delaware, Florida, Hawaii, Nebraska, Louisiana, New Mexico, New York, North Dakota, Ohio, Oregon and Tennessee.

It's too late at night to verify that, but I clicked on a picture of North Dakota, and am inspired to want to put up a contest thread for the ugliest state capitol building.

[Between the Lines]

Virginia and Ohio do have domes, but they are not visible from the exterior. Florida's capitol has two domes, one over each wing. Nebraska's capitol although a high rise building has a dome. That leaves us with nine - Delaware, Hawaii, Louisiana, New Mexico, New York, North Dakota, Alaska, Oregon and Tennessee, but Virginia and Ohio can be added if we are including only domes visible from the exterior, bringing the total to eleven. The plans for Alaska's new capitol building does include a dome.