I've tried searching on Ancestry which has a database "
England & Wales, Criminal Registers, 1791-1892"
From what you've written I take it you've read the article concerning the suicide attempt. I've searched The Chronicle but can't see any further references to suggest any court case.
English law perceived suicide (and attempts) as an immoral, criminal offence against God and also against the King. It first became illegal in the 13th century. Until 1822, in fact, the possessions of somebody who committed suicide could even be forfeited to the Crown. Suicide ceased to be a criminal offence with the passing of the Suicide Act 1961; the same Act made it an offence to assist in a suicide.
So you are correct that an 1828 act would be a crime.