A bench warrant is a bench warrant whether it is issued by a criminal court judge or a civil court judge.
A bench warrant is issued by the Court. A private citizen or his attorney isn't the originating agent, the Court (the judge) is. The Court has sole discretion in this, and cannot be compelled to issue a bench warrant.
bench warrant issued by judge
A bench warrant in ANY state is a warrant issued directly by the court, on its own authority, to take the named individual into custody.
Bench warrants are generally issued for violations of state law. A person may be arrested on a bench warrant in any part of the state where it is issued, or even in another state is the issuing state is willing to extradite the offender.
ALL states WILL EXTRADITE if the crime is severe enough to warrant such or, in most cases, failure to appear in court.
It's unlikely that they would extradite you back to NY. HOWEVER - there are interstate compacts in effect in which the states honor each others family court/support judgments and awards. NY COULD notify OR if you are in child support arrears, THEN you would be subject to prosecution in OR.
A "bench warrant" is a warrant issued by a judge on his sole authority. Only the judge who issued the warrant can vacate the warrant. If he had to issue one to get you to court to testify, you probably won't be released until after your necessity in the court action is ended.
Contact the court.
bench warrant
If a bench warrant is issued for you, you will be arrested immediately upon being located by the sheriff or police. If it is a 'normal' bench warrant you will be transported to jail and held for court the next day. If it is a "forthwith" order, you will immediately be transported directly to court and presented to the judge.
Appear. A warrant is an order from the court for something to be done. A bench warrant is a order to any police officer (which they must obey) to arrest and deliver a specific person to the court. Going in on your own should cancel the warrant, and may let you avoid arrest.