I have not come across the term before but found this in the Derbyshire Courier November 15, 1851:
It sounds like an event rather than a place. In many other references to Mansfield Statutes (and other statutes like Bolsover Statutes) that I found there were often mentions of servants being hired so that seems to have been something of a focus for it/them.
I also found this at the GENUKI page for Mansfield:
The Statute Fair for the hiring of servants was held on the first
Friday on November.
so it seems like hiring servants was its main purpose.
And from the Merriam-Webster online dictionary:
Definition of STATUTE FAIR
: an annual fair formerly held in English towns and villages for the
hiring of servants and farm laborers
There is also some interesting context provided by @alephzero that I think should be captured within this answer:
There was nothing equivalent to modern transport and communication
systems, and many of the servants, farm workers, etc being hired would
be functionally illiterate. So instead of the modern "continuous
recruitment" system, the standard contract for servants was employment
for "a year and a day", and job-swapping was done by physically
getting everybody in the community together on one day each year,
usually after the end of harvesting, when the workload on the farms
was low but the weather was still good enough to allow an all-day
open-air "recruitment event" to be practical.
Some of these annual fairs have been in existence since the 13th
century, and since they involved large scale public meetings, the
ruling classes were naturally concerned about the possibility of
insurrection, etc. Their dates and locations were therefore officially
regulated (in some cases, by Acts of Parliament) - hence the name
"statute fair", i.e., a public gathering which would otherwise be
illegal, but permitted by a legal statute.
Since all the employers were physically in one place on the same day,
it made sense to use the time for other things as well as recruitment
- for example trading animals between themselves, as opposed to selling animals to be slaughtered for food which was obviously a
regular necessity (e.g. at markets held once or twice each week).