Residency requirements for divorce depend on one spouse or the other living in a state before either of them can file there. This holds true for Missouri. Only one of you must live in the state, but you might have problems with certain aspects of your divorce if one of you resides elsewhere.
Missouri's Residency Requirement
Missouri's residency requirement for divorce is 90 days, so you can file for divorce about three months after you move to the state. The three months must occur right before you file. If you don't live in Missouri, but your spouse does, you can file if he's lived there for the last 90 days. Either way, you must have him officially served with your divorce papers, either in Missouri or in the state where he resides.
If you and your spouse don't both live in Missouri, you might hit a roadblock when it comes to the court dividing marital property. If the property is located outside the state, perhaps because you lived elsewhere then moved to Missouri to file, the court has no jurisdiction over it. Only a judge in the other state can decide who gets the property. Missouri courts can't decide issues of alimony unless the spouse who is asking for it lives there. As for custody, Missouri has adopted the Uniform Child Custody Jurisdiction and Enforcement Act, so the state generally only has jurisdiction over your children if the child has lived in the state for the last six months before you file.