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Reply by David Allen Lambert, NEHGS Chief Genealogist
The reports that you are seeking do exist. In fact they were recently digitized by the Massachusetts State Library in Boston, Massachusetts. You can utilize reports for the 1850's online, as well as other years. The collection online spans 1832 until 1953. The name of the hospital has changed over the years - State Lunatic Hospital (1832, 1833); State Lunatic Hospital at Worcester (1834-1884); Worcester Lunatic Hospital (1885-1898); Worcester Insane Hospital (1899-1908); and the Worcester State Hospital (1909-present).
To search the annual reports online go to the following website: http://www.mass.gov/anf/research-and-tech/oversight-agencies/lib/worcester-state-hospital.html