Why would you have a warrant in a state you have never been to?

It is possible to have a warrant for another state without having been physical present. For example, a person could have a warrant for crimes that can be committed remotely (telephone harassment, identity theft, so on) without physically being in the state where the crime was committed. It is also certainly possible the police had made a mistake and simply have a warrant for the wrong person. You can contest extradition if there is an identity issue. There also may be an issue with the extradition demand even if there is cause for a warrant if she was not physically present in the other state. When extradition is sought a a person was not physically present in the other state, C.R.S. § 16-19-107 controls. Your cousin needs a lawyer to go over the specifics of her case including what the basis for the warrant is, any identity issues, and challenging the extradition procedure.