Is there a divorce action pending? If so, you can set forth that custody agreement in your stipulated judgment. If you are not ready for judgment, you can draft a stipulation and order regarding your custody agreement and file that with the court. Otherwise, to take advantage of the court's free mediation services, you would need to have a motion pending regarding custody. i.e. when a party files a request for order re custody, the matter is first referred to mediation before the hearing date. Otherwise, you are free to hire a mediator or a lawyer to put your agreement in writing by drafting a stipulation or settlement agreement.
The short answer is no, you do not need to go to mediation if you have already reached a full agreement. What you need is either a stipulated order, or a judgment, depending on the permanency of your agreement. If you intend this custodial arrangement to be a final, permanent (absent a change of circumstances), agreement you will need a judgment. The type of judgment you require, and the steps needed to achieve it, will depend upon whether you and the other parent are legally married. I recognize that this may not fully answer your question, but is the best I can provide with the facts available. I would strongly suggest that you consult with an attorney, or that you and the other parent jointly retain a mediator who is an attorney, to further advise you concerning how best to proceed.
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