From the German Wikipedia page 
The city archives for Darmstadt, GThe city archives were probably founded in the late 16th century in the course of a modernization of the administration. The year 1565 is occupied by a chest for the storage of city accounts, documents, court books and the Stadtsiegel. This chest was first in the town church. In 1609 the archives were taken to the town hall. In 1688 a town hall archive is mentioned for the first time. In 1705, the name Stadtarchiv was used for the first time. In the 19th century the archives were stored on the attic of the town hall.
Since 1929, the City Archives has been an independent municipal office. The archive was at this time in Hügelstraße 26 / Ecke Schützenstraße. During the Second World War, the archives were stored in the basement of the former Ludwigsbahnhof at Steubenplatz. These stocks have largely been preserved. The Archivgebäude in the Hügelstraße was destroyed during an air attack in 1944.