The 1749 Court House is a museum right in the center of Plymouth that is free and filled with interesting items from Plymouth's history. It is the oldest wooden Court House and the longest used municipal building in America. (Taken from their website)

Currently used as office space for county government employees and officials. However, it is currently haunted by a miner named Miles Fuller who was convicted of killing another prospector.Miles was executed by hanging via the portable gallows which were set up in the yard, which was located on the north side of the jail behind the courthouse on May 18, 1906.

Throughout the years, an apparition looking just like Miles has been seen wandering around this same yard, by the back door of the courthouse ground floor.
(hauntedhouses.com)

The municipal museum of Colorado Springs, located in the former El Paso County Courthouse (1903), portrays the history and culture of the Pikes Peak Region in exhibits emphasizing the unique character of this uncommon Front Range community. As the focal point of the City's lovely downtown, the Colorado Springs Pioneers Museum draws thousands of people to the area annually. Centered in one of two primary downtown parks, this elegant and historic structure is surrounded by inviting green lawns, colorful flowers, outdoor sculptures, and a splendid granite fountain.
In the 1950's a goverment agency manger was murdered by one of his employees. To this day, the room's his department occupied are haunted, giving anyone who passes through them a feeling of uneasiness.