Probably. Washington will notify TDC if they don't intend to extradite. I would hire a defense attorney in Washington. They may be able to convince the DA the case is not worth the cost of extradition.
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Whether the demanding jurisdiction (Washington in this case) will extradite is a case-by-case question. The prosecutor there will decide whether it's worth the expense of resources to fly or drive to come and get the fugitive, based on many factors including the seriousness of the charge.
In Harris County, all extraditions to demanding jurisdictions are handled in County Criminal Court at Law Number 10, by Judge Sherman Ross. It has been this way for a very long time. It's good that the fugitive you're asking about signed a waiver. The law says that once he signs the waiver, he can only be held for a "reasonable time" awaiting extradition. In Judge Ross's court, that means Washington has fourteen (14) days to come get him. If they don't--barring any extraordinary circumstances that convince the court that further detention would remain "reasonable,"--he'll be released.
On the other hand, it he had refused to sign a waiver, he would have been held indefinitely while the governors offices of both Texas and Washington work out the procurement of a governor's warrant. These are rare, because most fugitives waive. I've only ever seen one. (They are pretty cool--the one I saw was signed by Rick Perry and Arnold Schwarzenegger!)
If the demanding jurisdiction wants you, it doesn't usually help to go this route, because they'll go through this trouble, and get the warrant. The fugitive just winds up staying in the Harris County jail longer--and there's no guarantee that the demanding jurisdiction will count this time toward any eventual sentence. Plus, a fugitive COULD challenge the validity of the warrant, but those challenges are tough to win because the requirements of the warrants are pretty low.
Odds are that your fugitive is already being represented by one of the very capable extradition specialists who practice in court 10. If you have any more questions, I'm certain they would be glad to explain the procedure more fully, and answer any other questions.
Finally, of course, even if released, the Washington charges will remain open until resolved. That means any time he's ever pulled over on traffic, or flies, etc. this same thing will happen. The best policy with these sorts of things is usually to be proactive. He should, whether extradited or not, employ a lawyer to handle his Washington case.
This question is more appropriately asked of a Washington criminal defense lawyer.
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