I have spoken with the current and former Town Clerk of Colebrook, NH - which the village of Kidderville is part of and whose ordinances it is obliged to abide by. They can find no mention of anything like this as far back as 1950. A history of Colebrook, written by Dr. William H. Gifford, suggests that the airport opened to the public in 1963.
As such, this particular claim cannot be substantiated.
The only likely candidate airport for this would be Gifford Field (Airport code 4C4) which is 7 miles from Kidderville:
Gifford Field is a single grass strip with a private owner, and as such has a rather rural character.
The former town clerk did, however, mention that a Dr. Gifford (after whom Gifford field is presumably named) was apparently rather a prankster in his day. Her theory is essentially that he started this as a joke and it therefore stands as a fairly early example of a viral meme that predates the internet.
TL;DR - No such ordinance likely ever existed, but a personality in the area likely started the myth as a joke.