I understand that there are records relating to the Civil War Draft Registration for Massachusetts available. Can you tell me where these records are kept?
The Civil War Draft Registration of 1863 that you mention are available. These were arranged by Congressional Districts throughout the Union states. These records were originally in the National Archives in Washington, D.C. but the New England volumes have been transferred to the New England Regional Branch of the National Archives in Waltham, Massachusetts. An article about these records appeared in the Waltham Historical Society newsletter can be read online as a PDF document: http://host24.hrwebservices.net/~watchci/WHSOC09/NovemberWeathervane.pdf
These records can be inspected upon a visit to NARA branch, for more information about this research facility: http://www.archives.gov/northeast/boston/ I personally inspected the pages relating to my hometown of Stoughton, Norfolk Co., Massachusetts and transcribed the pages associated. The questions that were requested for those from Stoughton included - Name, age, eye color, hair color, complexion, height, Where born “state or kingdom” and town or county, occupation, enrollment or service dates, and remarks. The remarks field often contains reasons that the draftee may not be able to serve due to medical conditions. If you would like to see an example of the answers to the questions that were asked, go to the following example of my transcriptions for Stoughton: http://www.stoughtonhistory.com/1863draft.htm