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.
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.