A dispute over a contract between two people in the same city would most likely be heard first in a state trial court. This is a court which has authorization to hear only specified types of cases and as the case is one of a contract it goes to the State Trial Courts due to the fact that it is not specific legal matter such as family, for instance.
A dispute over a contract between two people in the same city would most likely be heard first in a "local court", unless of course the dispute is over something very serious, such as a violent crime.
