A friend has a warrant for not paying the last of her fines for a DUI in Colorado and wants to go to Tijuana, Mexico. If Immigration checks and finds out (when she crosses the border on her way back) that she has a warrant, will they extradite her back to Colorado? She now lives in Wyoming.
It depends on whether Colorado has sent the warrant to the NCIC, so that it can be accessed by law enforcement anywhere in the US. If this has happened, then it means Colorado is likely to be willing to extradite, and CBP will be able to access the warrant at the border.
CBP officers also rely on the Interagency Border Inspection System (IBIS) to determine which individuals to target for secondary examination upon arrival in the United States.
IBIS provides the law enforcement community with access to computer-based enforcement files of common interest. It also provides access to the FBI's National Crime Information Center (NCIC) and allows its users to interface with all 50 states via the National Law Enforcement Telecommunications Systems.
Which means that even if Colorado hasn't sent it to NCIC and isn't willing to extradite, CBP may still be aware of the warrant through NLETS. This means she'll at least be subject to secondary inspection and a very unpleasant border crossing, even if she is ultimately admitted without being arrested.
The best thing to do is to clear this up before the trip, if possible.