I found out that my house was built sometime between 1871 and 1873, somewhere in there. Because of the tax assessment for my house did not show up in the 1869-71 assessment, but big as day in the 1872-1873 assessment as a brick house worth $1000. These assessments are located on microfilm at the MLK library in the Washingtonia division. Well at least the 1874ish one. 1860something to whenever in the 19th Century is located at the National Archives downtown, record group 351, entry 49 (or 46, 40something, I forget). I don’t know if the Washington, DC Historic Society has it too.
If you are going to look at property assessments know your square number and your lot number by heart. It also helps to know around about what time your lot existed. My block in the late 18th century was subdivided into 6 to 8 lots. In the late 19th century it was divided further and my lot became into existence.