Most states in the US do not have separate state aircraft registries. That is, a valid FAA registration is enough to safely operate and own the aircraft in the state in which its base. That said, there are several states, a handful, that have independent aircraft registries that are required, such as the State of Indiana. The State of Florida has a form that you need to file that I believe they call an aircraft registry. Whether or not your aircraft needs to be registered in the state in which you’re based is, ultimately, a question of state law. It’s also often a question, such as the State of Indiana, of what do you mean by based and how many days a year the aircraft is going to spend there. Taking a look at the newest regulation is often very helpful in determining whether or not you need to complete not only an FAA regulation for an aircraft, but also a state registration.