What US State is the only one with a legislature made up of a single house (unicameral)?

Nebraska was admitted as the 37th state of the United States in 1867. It is the only state in the United States whose legislature is unicameral and officially nonpartisan. Senator George Norris proposed the idea in 1934 and it was implemented in 1937. It was a method of saving money (which it successfully did). As a result the legislature went down to (then) 43 members from 133 resulting in a far more efficient House. All members are known as Senators. Uniquely, the Legislature is non-partisan.

On efficiency grounds there is much to be said for a unicameral system. In fact, there is not much to be said against it! The one-house system was more efficient than its bi-cameral predecessor. The number of committees was pared down from 61 to 18, and 581 bills were introduced in 1937, as opposed to twice that many the previous session. The last bicameral session in 1935 ran 110 days, passed 192 bills and cost $202,593. The first unicameral session two years later ran 98 days, passed 214 bills and cost $103,445.