Check with an attorney who practices in Washington to be sure (assuming your judgment was from Washington). In Oregon, if both parents consent, then I don't think you need to file anything. It'd be a good idea to get a statement of his consent in writing (an email in which he says so would be fine).
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If your judgment is from Oregon, it would be wise to file your written 60-day notice with the father and with the court, then get his written consent to the move. This will cover you in case he decides to change his mind later on. If your judgment is from Washington, consult an attorney licensed to practice in Washington.
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