Written court records are taken for all proceedings. If you're looking for specific court record but you don't know which court the case appeared at, the best place to start are the criminal registers for England and Wales 1791 to 1892 held at National Archives (search for '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 or Petty Sessions.
The criminal registers are also available on Ancestry. Free access is available at any of our libraries.
Another option is to try the digital archive of the Manchester Guardian newspaper via our online reference library to see if the case was reported. Free access is available for library members.