What do you mean "referred locally"?
If a passenger has a warrant out of Texas and he lands in Chicago, CBP doesn't hand him over to the Chicago Police Department. CBP is responsible for the extradition (if that's what Texas wants).
I guess Chicago and some other states are different but that is exactly what happens in NY...they are handed to the local jurisdiction to process as a "fugitive from justice" and then extradited. Again, this only takes place IF the issuing agency says they will extradite.