THE MANCHESTER ROOM@CITY LIBRARY AND GREATER MANCHESTER COUNTY RECORD OFFICE (WITH MANCHESTER ARCHIVES) OPEN ON 28 JUNE 2010.
The best place to start, if you do not know which court the case appeared at, is the Criminal Registers for England and Wales 1791-1892 held at National Archives (HO 27). The registers will tell you whether the case was held at the Assizes or Quarter Sessions. However they do not include Magistrates Courts / Petty Sessions.
The Criminal Registers have been digitised and are available on Ancestry.com (subscription web site). Free access to Ancestry Library Edition is available at the Manchester Room@City Library and any City of Manchester library.
Another option is to try the digital archive of the Manchester Guardian to see if the case was reported. Free access to this is available for library members in our 24 Hour Library.