Slavery is legal in nearly every city-state in the world. In most it is reluctantly accepted, but in some it is a major trade and accepted whole heartedly.
Some of the exceptions:
In Purity, slavery is illegal. The owning, selling or transporting of slaves into or through Purity will result in the freedom of the slave and imprisonment for the slave owner (sometimes mitigated by a hefty fine). This causes escaped slaves to flock to Purity where they can be reasonably safe from recapture.
Myork has outlawed the sale of slaves, but not the owning of slaves. This means that slaves bought elsewhere can be brought into Myork and held. The ban on the sale/purchase was intended to minimize the slave trade in Myork, and along with the cultural pressure against it, slavery in Myork is minimal. Myork also banned the trade in “dangerous animals”. The Myork courts were not sure how to handle the slave trade in minotaurs and some other “monstrous peoples”, so they have banned the sale of both. The sale of slaves and dangerous animals is allowed in Revolution City, and there is a slave auction there, but this is not spoken of in Myork. The Myork Navy does allow slave traders to sail out of the port, trade in slaves on the open water, and then return to port. This is seen as “trade on the high seas” and is not restricted by what are seen as the standard rules of trade outside the city-states. These ships are charged an additional docking fee for returning to port, but this fee is not enough to deter the practice.
The Barony of Hollywood in the Council of Baronies has discussed the idea of banning slavery within its borders, but has not done so yet. The reasoning behind such a move was to encourage escaped slaves to flock to Hollywood where they are in desperate need for workers. The other barons have blocked Hollywood for the time being, but probably not forever. With a misunderstanding of the current laws, some escaped slaves have already started moving to Hollywood.
Helatia is one of the few city-states with laws protecting the rights of slaves, but this has served to encourage slave ownership in the city-state as it does not have the social stigma it has in many other places.
Snobist, Rhum, Parnania and Villai allow slavery but it is socially/culturally frowned upon. This means that there are few slaves in the cities themselves, but many of the largest farms will use slave labor.