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Jurisdiction could be in either place, depending on why you want to sue. You stated that a company owes you money. If certain portions of the transaction took place in Illinois, then you may have a basis to sue in Connecticut. However, there are two forms of jurisdiction a court needs in order to rule against someone. They require subject matter jurisdiction, meaning that the issue is something they can discuss and they need personal jurisdiction.
If events took place in Illinois, then the court would certainly have subject matter jurisdiction. The issue though would be personal jurisdiction. The company would have to have some presence in Illinois or be served with service of process in Illinois. That's much harder to do.
So, the easiest thing is usually to sue the person or company in the state where they are located, because then there can be no issue about jurisdiction over the person and a service of process is simpler. Yes, it means you'll have to travel for the hearing, but that's just a single event. Most everything else can be done by computer or phone (getting the filing documents and service or process completed).
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