The father cannot keep you from moving out of state without a court document, but that doesn't mean you should move without consulting a lawyer regarding the potential consequences of your actions. If paternity has been established, the father may be able to file and obtain a temporary protective order of restraint quickly that orders the return of the child to Oregon. If the father acts quickly, he may be able to get a court order requiring you to move back.
You should review the facts and your situation with a local attorney to help prevent your move from turning into a legal battle.
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