A court of justice is the government's power, set out in stone and marble, for the people to respect and fear.
As such, the building adds significantly to the repression of the people in the region where it stands. Further, because of the forces of law and order are in intimate partnership with the government's tax gatherers, a law court gives their demands for money even more force. The tax gathered in a region also increases thanks to the court. Finally, the judges here have the power to use civil law to help the military's authority and this means that they can aid military recruitment, if only by the simple expedient of sentencing wrongdoers to the ranks!
Social order is often more important than any amount of so-called liberty to the smooth running of a nation. To modern eyes, a court of justice was surprisingly parsimonious with the justice it dispensed: its purpose was to enforce laws that protected the status quo, which did not have to be the same thing as "justice". Receiving justice depended more upon the social class of the defendant or plaintiff, and less upon clever legal argument or the law itself. Even in countries that prided themselves on "liberty", such as Britain, the law courts were more interested in protecting the rights of property rather than the rights of common and poor men.
Building Courts of Justice requires pre-existing Magistrates, and cost 3,000 gold and 7 turns. Public Schooling must also be researched before Courts of Justice become available. Alternatively, it is possible to convert third-tier military, ordnance, or cultural buildings to Courts of Justice for the same cost, though doing so is less cost-efficient.
Like all other administrative buildings, the Court of Justice's increase to tax income does not have a negative impact on public order, but it does increase the penalty on town wealth growth. Unless it is exempted from tax entirely, a region with a Court of Justice has a slower wealth growth than a region without one. A region without an administrative building, on the other hand, can't exploit its taxable income as fully. In some cases, it may be worth delaying building an administrative building in a region until its wealth has built up somewhat, to increase income in the long run.
Courts of Justice may be upgraded to Courts of Appeals, which provide a higher tax rate bonus, furthers the civil branch of the technology tree, and provides higher repression to its region.