It would depend on the particular state law you are asking about.
If you are asking about in Arizona, it would require the consent of the parents and a court order authorizing the marriage, the code section is below for your review. I will highlight the area of law. I also want to let you know that you can only get married in the state if you meet their residency requirements (if any). But to answer your question for a minor child it would require consent by the parents and the court.
25-102. Consent required for marriage of minors
A. Persons under eighteen years of age shall not marry without the consent of the parent or guardian having custody of such person. Persons under sixteen years of age shall not marry without the consent of the parent or guardian having custody of that person and the approval of any superior court judge in the state. When both parents are living the consent of either parent is sufficient. When the parents are living apart, the consent shall be given by the parent who has the custody of the minor.
B. Before authorizing the marriage of a person who is under sixteen years of age, the court:
1. Shall require both parties to the marriage to complete premarital counseling. The court may waive this requirement if the court determines that premarital counseling is not reasonably available.
2. Must find that the minor is entering into the marriage voluntarily.
3. Must find that the marriage is in the best interests of the minor under the circumstances.
4. May require that the minor continue to attend school.
5. May require any other condition that the court determines is reasonable under the circumstances.
C. A marriage shall not take place under this section if it is prohibited by the law relating to prohibited and void marriages.
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