Overland Park Police Chief John Douglass said at a news conference Sunday that the person who had been reported to be in critical condition was one of the three dead.
Douglass said shots were fired behind the Jewish Community Center of Greater Kansas City in a parking lot, and two males died. Shots were reported minutes later at the Village Shalom retirement community, where one female died.
Ages and identities of the victims were not released.
A man in his 70s who is not from Kansas was taken into custody at a nearby school. Douglass did not provide further information.
Douglass said a shotgun was involved.