Yes — Connecticut regulation 19-13-B33b requires a readily available telephone or device for emergency use at public pools.
Connecticut requires a telephone or suitable communication device to be readily available at all public pools for emergency use.
Citation: 19-13-B33b
"Suitable device" gives some flexibility to use a cellular emergency phone instead of a traditional landline, useful for pools without existing phone wiring. The key requirement is that it works reliably and is accessible without delay.
SouthEast Telephone installs and monitors cellular emergency pool phones nationwide and can help you meet Connecticut's requirements.