The first reference to the Campbelltown spelling that we could find was in 1830. Prior to this both Campbell Town and Campbell-town were used. Throughout the 1830s all three versions: the 2 worded name, the hyphenated name and today's spelling were used as much as one another. By the late 1830s and into the 1840s, Campbell Town was becoming a more infrequent way of spelling. It gradually became more infrequent through the 1850s to the 1870s, with only the very occasional spelling this way. By the 1880s it had all but disappeared.
There doesn't appear to be any official announcement or ruling on the change of spelling. Rather, the Campbelltown form of spelling appears to be simply the result of a morph from one version to the next or a corruption of the original two worded version.
An 1829 article from the Sydney Gazette