City and towns in Massachusetts keep their own vital records but have sent transcripts or copies to the State since 1841.

• For records after 1906 - see Massachusetts Department of Public Health - Registry of Vital records and Statistics.
  
  
• For records between 1841 and 1905 - see the Massachusetts State Archives

  The records from 1841 to 1903 are in register-type bound books.
  Starting in 1903 death records became individual certificates and in the 1920s birth and marriage records also became individual certificates.

• For pre-1841 records try the city clerk's office:
  

  Medford City Clerk's Office
  85 George P Hassett Dr
  Medford, MA 02155-3256
  (781) 393-2425
  

Other alternatives:
Massachusetts Vital Records to 1850 (microform)
compiled by Jay Mack Holbrook "Filmed from original town records" - should include Medford 1673-1849
Boston Public Library   Microtext Dept.  call #  F63.M485 1982x

Vital records of Medford Massachusetts, to the year 1850 (book)
Publisher : Boston, Mass., Pub. by the New England historic genealogical society; at the charge of the Eddy town record fund, 1907. Available at the Medford Public Library.

Mass. Genealogical Research is a private business that will do research for a fee, but they have an excellent information page on obtaining Massachusetts Vital Records for yourself. (This is not an endorsement of their services.)