Yes — New Hampshire rule Env-Dw 1103.05 requires an emergency telephone with prominently posted numbers.
New Hampshire requires an emergency telephone with prominently posted emergency numbers.
Citation: Env-Dw 1103.05
The "prominently posted" requirement means a small, hard-to-read sticker likely won't pass inspection — use a clearly visible, weather-resistant sign next to the phone.
SouthEast Telephone installs and monitors cellular emergency pool phones nationwide and can help you meet New Hampshire's requirements.