The map is sourced from Wikipedia, which has multiple articles regarding this topic.
For California, requirements for "an unmarried person under 18 years of age" are:
Get permission via court order
Proof of filing written consent from one parent/guardian of each underage person, or court permission if no parent/guardian exists who is capable of consenting
If a minor is under 15 and/or has no high school graduation/GED: An investigation by Family Court Services recommending the marriage after ruling out "potential force, threat, persuasion, fraud, coercion, or duress" by any person involved, after interviewing each person to be married and one parent/guardian (if applicable). (If these are not ruled out, a report to child protective services must be made.)
If a minor is under 15 and/or has no high school graduation/GED: A filmed second interview with each person involved
If a minor is under 15 and/or has no high school graduation/GED: The court separately considering "whether there is evidence of coercion or undue influence on the minor"
If under 15 and/or has no high school graduation/GED and/or with no pregnancy involved: A minimum 30 day waiting period
The court considering whether to require premarital counseling, which cannot be required to be from any religious organization
Further information to be provided to the court about the two people to be married, with information provided to "the minor" regarding emancipation and rights of an emancipated minor, divorce, numbers for the National Domestic Violence Hotline and the National Sexual Assault Hotline
Note that, though the California statutes apply to marriages between two minors, they sometimes refer to "the minor" as if assuming there is only one in the marriage.
News site California Health Report contrasts data from the state compared to a study conducted by anti-child-marriage nonprofit Unchained. The news article quotes a statement from the ACLU that opposes changing the law, out of worries that child marriages will be done under the radar, but I could not independently verify that this quote is legitimate.
In New Mexico*, the requirements for marriage for "any person under sixteen years of age" (with separate requirements for ages 16-17) are:
The children's or family division of the district court authorizes the marriage
A parent/guardian of the minor requests the marriage "to compel support and establish parentage" OR one of the marriage partners is pregnant
The annotations to the New Mexico law mention that the law previously did not allow females 14 and under to marry, but that this was repealed in 1978. ChildUSA, cited below, states that no proof of age is required, but the statute appears to require examining the minor's birth certificate to determine parentage.
*Link is not a .gov site but is endorsed as the official state law database here
In Oklahoma, the requirements for marriage of any "person under the age of sixteen (16) years" (with separate requirements for ages 16-17) are:
The marriage is part of "settlement of a suit for seduction or paternity," OR all of the following apply:
A pregnancy is involved or the illegitimate child has already been born
At least one parent/guardian of each minor (if not in custody) presents in court and has the opportunity to object (if not present, they may be given notice of the hearing)
Note that the Oklahoma statute is written in a way that is difficult to interpret for a layperson like me, so the above may contain caveats. I also do not see "seduction" defined in the definitions list in the statute. FindLaw interprets this statute simply as "Minors under 16 may obtain license in case of pregnancy or birth of child with parental consent and court authorization." Oklahoma also bans same-sex marriage in the same statute, so presumably this would not apply for same-sex underage marriages. I am not a lawyer and this is not legal advice.
In Mississippi*, the requirements for marriage in the case that "the male applicant is under seventeen (17) years of age or the female is under fifteen (15) years of age" (with separate requirements for males aged 17-21 or females aged 15-21) are:
The court receives proof that the marriage is willing and "sufficient reasons exist"
The parents/guardian of each minor consents
Neither partner is intoxicated or seems to the clerk to be mentally incapable of consenting to marriage
Mississippi bans same-sex marriage in the same statute, so presumably this would not apply for same-sex underage marriages.
*Link is not a .gov site but is endorsed as the official state law publisher here
A report published by ChildUSA, a think tank advocating against child abuse, offers an overview condemning child marriage in the USA, which also goes state-by-state. It states that "there is no federal law banning child marriage" and points to Washington as another state which does not have an age requirement. US territories without an age requirement are listed as Guam, N.M.I., and Puerto Rico. It also brings up that child marriage can occur in the 28 states that do not require "official proof of age for all applicants."
A consideration raised by a 2022 study in the Journal of Adolescent Health compared statutory rape laws to child marriage laws by state, also mentioning when the laws did not apply specifically due to a provision in the law regarding marital rape. By state:
In California, laws regarding rape don't apply only if one party in the marriage "is incapable of giving legal consent because of mental disorder or developmental or physical disability." Statutory rape laws explicitly do not apply for spouses.
In Mississippi, pedophilia law and statutory rape law explicity do not apply if the child is the adult's spouse. Sexual battery charges seem to still apply, however - which is to say, sexual penetration is illegal without consent, or for ages 14-16 if the perpetrator is 3 years older than the victim, or for any child 13 or under if the perpetrator is 2 years older than the victim. Pornography is also prohibited from distribution to anyone under 18 in all cases. Additionally, "No person shall, by any means including computer, knowingly entice, induce, persuade, seduce, solicit, advise, coerce, or order a child to meet with the defendant or any other person for the purpose of engaging in sexually explicit conduct." (Definitions for this statute were repealed.)
I'm afraid this is too much for me to continue deep-diving right now, and I'm not sure whether Tumblr will censor this entire topic.