Strictly speaking legally no, a helmet is not required as both the Nippi and Trippi are regarded as trikes and so are therefore are exempt. However in practice its still advisable to wear one, particularly on a Trippi. Just because you ride carefully others don't always drive with the same care!
Besides a crash helmet and visor will offer some protection against the weather and objects that fly up from the road too. And no one intends to have an crash, but that's why they call them accidents!