Any person desiring to adopt another person may petition the court or family court where the person seeking to adopt resides or where the person to be adopted may be. The court or family court has exclusive original jurisdiction in proceedings for the adoption of a person. 

Missouri Statutes Regarding Adoption Of A Person

Statutes: 192.016, 193.087, 193.125, 193.265, 210.566, 210.822, 211.031, 211.177, 211.444, 211.447, 211.464, Chapter 453, 506.100506.150 and 506.160, RSMo

Procedures in Adoption Actions
 Administrative Order 14-03

All adoption petitions shall be filed in Judicial Records, Family Justice Center, 625 East 26th Street, Kansas City, Missouri, 64108.