Yes — Missouri rule 19 CSR 20-34.040 requires a phone accessible within 200 feet of the pool.
Missouri requires the emergency telephone to be accessible within 200 feet of the pool.
Citation: 19 CSR 20-34.040
200 feet is a fairly generous radius, so many properties can use a phone in a nearby clubhouse or office as long as it is clearly marked and within that distance.
SouthEast Telephone installs and monitors cellular emergency pool phones nationwide and can help you meet Missouri's requirements.