According to the City of Nelson website here,
Nelson's courthouse was designed by F.M. Rattenbury, the famous architect of British Columbia's Parliament Buildings and the Empress Hotel in Victoria. This building was completed at a cost of $109,145.88 in 1909 (the 1908 date stone is correct). It is a fine example of Beaux Arts Chateau style architecture with its high pitched roof, towers and conical caps, gables and paired windows.
You can read more about Francis Rattenbury on the Heritage B.C. site here.