Yes, they can. Will they? It may be a budgetary decision. When I was a prosecutor I would leave the warrant active. The guy would get arrested. I wouldn't extradite for 3d deg felonies and I would release him but leave the warrant active. The guy would keep getting arrested and released until he got tired of it and paid his own way to clear up the warrant.
I agree with my colleague. For many states, it is a budgetary concern because extradtions can be expensive. However, since you know abot the warrant, you should take steps to clear it. Even if CT doesn't extradite, you can keep getting arrested and sit in jail until CT elects not to extradite. It can keep happening until you clear the warrant because it wont' go away.
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